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Choonkil Park - One of the best experts on this subject based on the ideXlab platform.
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bi additive s functional inequalities and quasi multipliers on Banach Algebras
Bulletin of the Brazilian Mathematical Society New Series, 2019Co-Authors: Choonkil ParkAbstract:In this paper, we solve the following bi-additive s-functional inequalities where s is a fixed nonzero complex number with $$|s |< 1$$ , and where s is a fixed nonzero complex number with $$|s |< 1$$ . Moreover, we prove the Hyers–Ulam stability of quasi- $$*$$ -multipliers on Banach $$*$$ -Algebras and unital $$C^*$$ -Algebras, associated with the bi-additive s-functional inequalities (1) and (2).
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additive s functional inequality and hom derivations in Banach Algebras
Journal of Fixed Point Theory and Applications, 2019Co-Authors: Choonkil Park, Xiaohong ZhangAbstract:In this paper, we introduce and solve the following additive s-functional inequality: 0.1 $$\begin{aligned} \left\| f\left( x+y\right) - f(x )- f(y)\right\| \le \Vert s (f(x-y)-f(x)-f(-y))\Vert , \end{aligned}$$ where s is a fixed nonzero complex number with $$|s|<1$$ . Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of the additive s-functional inequality (0.1) in complex Banach spaces. Furthermore, we prove the Hyers–Ulam stability of hom-derivations in complex Banach Algebras.
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bi additive s functional inequalities and quasi multipliers on Banach Algebras
Mathematics, 2018Co-Authors: Choonkil ParkAbstract:Using the fixed point method, we prove the Hyers-Ulam stability of quasi-∗-multipliers on Banach ∗-Algebras and unital C*-Algebras, associated to bi-additive s-functional inequalities.
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fixed points and stability of the cauchy jensen functional inequality in fuzzy Banach Algebras
Applied Mathematics Letters, 2011Co-Authors: Choonkil ParkAbstract:Abstract Using the fixed point method, we prove the Hyers–Ulam stability of the Cauchy–Jensen functional inequality in fuzzy Banach Algebras.
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hyers ulam rassias stability of homomorphisms in quasi Banach Algebras
Bulletin Des Sciences Mathematiques, 2008Co-Authors: Choonkil ParkAbstract:Abstract In this paper, we prove the Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach Algebras. This is applied to investigate isomorphisms between quasi-Banach Algebras.
Nikolai Vasilevski - One of the best experts on this subject based on the ideXlab platform.
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on the structure of commutative Banach Algebras generated by toeplitz operators on the unit ball quasi elliptic case ii gelfand theory
Complex Analysis and Operator Theory, 2015Co-Authors: Wolfram Bauer, Nikolai VasilevskiAbstract:Extending our results in Bauer and Vasilevski (J Funct Anal 265(11):2956–2990, 2013) the present paper gives a detailed structural analysis of a class of commutative Banach Algebras \(\mathcal {B}_k(h)\) generated by Toeplitz operators on the standard weighted Bergman spaces \(\mathcal {A}_{\lambda }^2(\mathbb {B}^n)\) over the complex unit ball \(\mathbb {B}^n\) in \(\mathbb {C}^n\). In the most general situation we explicitly determine the set of maximal ideals of \(\mathcal {B}_k(h)\) and we describe the Gelfand transform on a dense subalgebra. As an application to the spectral theory we prove the inverse closedness of Algebras \(\mathcal {B}_k(h)\) in the full algebra of bounded operators on \(\mathcal {A}_{\lambda }^2(\mathbb {B}^n)\) for certain choices of \(h\). Moreover, it is remarked that \(\mathcal {B}_k(h)\) is not semi-simple. In the case of \(k=(n)\) we explicitly describe the radical \(\hbox {Rad}\, \mathcal {B}_n(h)\) of the algebra \(\mathcal {B}_n(h)\). This result generalizes and simplifies the characterization of \(\hbox {Rad}\,\mathcal {B}_2(1)\), which was given in Bauer and Vasilevski (Integr Equ Oper Theory 74:199–231, 2012).
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on the structure of commutative Banach Algebras generated by toeplitz operators on the unit ball quasi elliptic case i generating subAlgebras
Journal of Functional Analysis, 2013Co-Authors: Wolfram Bauer, Nikolai VasilevskiAbstract:Abstract Extending recent results in [3] to the higher dimensional setting n ⩾ 3 we provide a further step in the structural analysis of a class of commutative Banach Algebras generated by Toeplitz operators on the standard weighted Bergman space over the n -dimensional complex unit ball. The Algebras B k ( h ) under study are subordinated to the quasi-elliptic group of automorphisms of B n and in terms of their generators they were described in [23] . We show that B k ( h ) is generated in fact by an essentially smaller set of operators, i.e., the Toeplitz operators with k -quasi-radial symbols and a finite set of Toeplitz operators with “elementary” k -quasi-homogeneous symbols. Then we analyze the structure of the commutative subAlgebras corresponding to these two types of generating symbols. In particular, we describe spectra, joint spectra, maximal ideal spaces and the Gelfand transform.
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commutative toeplitz Banach Algebras on the ball and quasi nilpotent group action
Integral Equations and Operator Theory, 2012Co-Authors: Wolfram Bauer, Nikolai VasilevskiAbstract:Studying commutative C*-Algebras generated by Toeplitz operators on the unit ball it was proved that, given a maximal commutative subgroup of biholomorphisms of the unit ball, the C*-algebra generated by Toeplitz operators, whose symbols are invariant under the action of this subgroup, is commutative on each standard weighted Bergman space. There are five different pairwise non-conjugate model classes of such subgroups: quasi-elliptic, quasi-parabolic, quasi-hyperbolic, nilpotent and quasi-nilpotent. Recently it was observed in Vasilevski (Integr Equ Oper Theory. 66:141–152, 2010) that there are many other, not geometrically defined, classes of symbols which generate commutative Toeplitz operator Algebras on each weighted Bergman space. These classes of symbols were subordinated to the quasi-elliptic group, the corresponding commutative operator Algebras were Banach, and being extended to C*-Algebras they became non-commutative. These results were extended then to the classes of symbols, subordinated to the quasi-hyperbolic and quasi-parabolic groups. In this paper we prove the analogous commutativity result for Toeplitz operators whose symbols are subordinated to the quasi-nilpotent group. At the same time we conjecture that apart from the known C*-algebra cases there are no more new Banach Algebras generated by Toeplitz operators whose symbols are subordinated to the nilpotent group and which are commutative on each weighted Bergman space.
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quasi radial quasi homogeneous symbols and commutative Banach Algebras of toeplitz operators
Integral Equations and Operator Theory, 2010Co-Authors: Nikolai VasilevskiAbstract:We present here a quite unexpected result: Apart from already known commutative C*-Algebras generated by Toeplitz operators on the unit ball, there are many other Banach Algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last Algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C*-algebra, and for n = 1 all of them collapse to the algebra generated by Toeplitz operators with radial symbols.
Thomas Ransford - One of the best experts on this subject based on the ideXlab platform.
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real interpolation of Banach Algebras and factorization of weakly compact homomorphisms
Journal of Functional Analysis, 2004Co-Authors: Ariel Blanco, Sten Kaijser, Thomas RansfordAbstract:Abstract We consider the problem of when the real interpolation method respects Banach-algebra structure. Using our results, we show that every weakly compact homomorphism between Banach Algebras factors through a reflexive Banach algebra.
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Weakly compact homomorphisms
Transactions of the American Mathematical Society, 1992Co-Authors: José E. Galé, Thomas Ransford, Michael C. WhiteAbstract:We study the structure of weakly compact homomorphisms between Banach Algebras. In particular, it is shown that between many pairs of Algebras, the only weakly compact homomorphisms are those of finite rank
Aref Jeribi - One of the best experts on this subject based on the ideXlab platform.
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nonlinear functional analysis in Banach spaces and Banach Algebras fixed point theory under weak topology for nonlinear operators and block operator matrices with applications
2015Co-Authors: Aref Jeribi, Bilel KrichenAbstract:Fixed Point Theory Fundamentals Basic Tools in Banach Spaces Contraction Mappings Weak Topology Measure of Weak Noncompactness (MNWC) Basic Tools in Banach Algebras Elementary Fixed Point Theorems Positivity and Cones Fixed Point Theory under Weak Topology Fixed Point Theorems in DP Spaces and Weak Compactness Banach Spaces and Weak Compactness Fixed Point Theorems and MNWC Fixed Point Theorems for Multi-valued Mappings Some Leray-Schauder's Alternatives Fixed Point Theory in Banach Algebras Fixed Point Theorems Involving Three Operators WC-Banach Algebras Leray-Schauder's Alternatives in Banach Algebras Involving Three Operators Convex-Power Condensing Operators ws-Compact and omega-Convex-Power Condensing Maps Fixed Point Theory for BOM on Banach Spaces and Banach Algebras Some Variants of Schauder's and Krasnosel'skii's Fixed Point Theorems for BOM Fixed Point Theory under Weak Topology Features Fixed Point Theorems for BOM in Banach Algebras Fixed Point Results in a Regular Case BOM with Multi-Valued Inputs Applications in Mathematical Physics and Biology Existence of Solutions for Transport Equations Transport Equations in the Kinetic Theory of Gas Transport Equations Arising in Growing Cell Population Existence of Solutions for Nonlinear Integral Equations Existence of Solutions for Hammerstein's Integral Equation A Study of Some FIEs in Banach Algebras Existence Results for FDEs in Banach Algebras An Application of Leray-Schauder's Theorem to FIEs Two-Dimensional Boundary Value Problems A System of Transport Equations in Lp (1 ) A Study of a Biological Coupled System in L1 A Coupled Functional Integral System in Banach Algebras A Coupled System in Banach Algebras under the Condition (P) Nonlinear Equations with Unbounded Domain Differential Inclusions
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fixed point theorems of block operator matrices on Banach Algebras and an application to functional integral equations
Mathematical Methods in The Applied Sciences, 2013Co-Authors: Najib Kaddachi, Aref Jeribi, Bilel KrichenAbstract:In this paper, we study some fixed point theorems of a 2 × 2 block operator matrix defined on nonempty bounded closed convex subsets of Banach Algebras, where the entries are nonlinear operators. Furthermore, we apply the obtained results to a coupled system of nonlinear equations. Copyright © 2012 John Wiley & Sons, Ltd.
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new fixed point theorems in Banach Algebras under weak topology features and applications to nonlinear integral equations
Journal of Functional Analysis, 2010Co-Authors: Afif Ben Amar, Soufiene Chouayekh, Aref JeribiAbstract:We introduce a class of Banach Algebras satisfying certain sequential condition (P) and we prove fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators. Later on, we give some examples of applications of these types of results to the existence of solutions of nonlinear integral equations in Banach Algebras.
Wolfram Bauer - One of the best experts on this subject based on the ideXlab platform.
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on the structure of commutative Banach Algebras generated by toeplitz operators on the unit ball quasi elliptic case ii gelfand theory
Complex Analysis and Operator Theory, 2015Co-Authors: Wolfram Bauer, Nikolai VasilevskiAbstract:Extending our results in Bauer and Vasilevski (J Funct Anal 265(11):2956–2990, 2013) the present paper gives a detailed structural analysis of a class of commutative Banach Algebras \(\mathcal {B}_k(h)\) generated by Toeplitz operators on the standard weighted Bergman spaces \(\mathcal {A}_{\lambda }^2(\mathbb {B}^n)\) over the complex unit ball \(\mathbb {B}^n\) in \(\mathbb {C}^n\). In the most general situation we explicitly determine the set of maximal ideals of \(\mathcal {B}_k(h)\) and we describe the Gelfand transform on a dense subalgebra. As an application to the spectral theory we prove the inverse closedness of Algebras \(\mathcal {B}_k(h)\) in the full algebra of bounded operators on \(\mathcal {A}_{\lambda }^2(\mathbb {B}^n)\) for certain choices of \(h\). Moreover, it is remarked that \(\mathcal {B}_k(h)\) is not semi-simple. In the case of \(k=(n)\) we explicitly describe the radical \(\hbox {Rad}\, \mathcal {B}_n(h)\) of the algebra \(\mathcal {B}_n(h)\). This result generalizes and simplifies the characterization of \(\hbox {Rad}\,\mathcal {B}_2(1)\), which was given in Bauer and Vasilevski (Integr Equ Oper Theory 74:199–231, 2012).
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on the structure of commutative Banach Algebras generated by toeplitz operators on the unit ball quasi elliptic case i generating subAlgebras
Journal of Functional Analysis, 2013Co-Authors: Wolfram Bauer, Nikolai VasilevskiAbstract:Abstract Extending recent results in [3] to the higher dimensional setting n ⩾ 3 we provide a further step in the structural analysis of a class of commutative Banach Algebras generated by Toeplitz operators on the standard weighted Bergman space over the n -dimensional complex unit ball. The Algebras B k ( h ) under study are subordinated to the quasi-elliptic group of automorphisms of B n and in terms of their generators they were described in [23] . We show that B k ( h ) is generated in fact by an essentially smaller set of operators, i.e., the Toeplitz operators with k -quasi-radial symbols and a finite set of Toeplitz operators with “elementary” k -quasi-homogeneous symbols. Then we analyze the structure of the commutative subAlgebras corresponding to these two types of generating symbols. In particular, we describe spectra, joint spectra, maximal ideal spaces and the Gelfand transform.
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commutative toeplitz Banach Algebras on the ball and quasi nilpotent group action
Integral Equations and Operator Theory, 2012Co-Authors: Wolfram Bauer, Nikolai VasilevskiAbstract:Studying commutative C*-Algebras generated by Toeplitz operators on the unit ball it was proved that, given a maximal commutative subgroup of biholomorphisms of the unit ball, the C*-algebra generated by Toeplitz operators, whose symbols are invariant under the action of this subgroup, is commutative on each standard weighted Bergman space. There are five different pairwise non-conjugate model classes of such subgroups: quasi-elliptic, quasi-parabolic, quasi-hyperbolic, nilpotent and quasi-nilpotent. Recently it was observed in Vasilevski (Integr Equ Oper Theory. 66:141–152, 2010) that there are many other, not geometrically defined, classes of symbols which generate commutative Toeplitz operator Algebras on each weighted Bergman space. These classes of symbols were subordinated to the quasi-elliptic group, the corresponding commutative operator Algebras were Banach, and being extended to C*-Algebras they became non-commutative. These results were extended then to the classes of symbols, subordinated to the quasi-hyperbolic and quasi-parabolic groups. In this paper we prove the analogous commutativity result for Toeplitz operators whose symbols are subordinated to the quasi-nilpotent group. At the same time we conjecture that apart from the known C*-algebra cases there are no more new Banach Algebras generated by Toeplitz operators whose symbols are subordinated to the nilpotent group and which are commutative on each weighted Bergman space.
