The Experts below are selected from a list of 246 Experts worldwide ranked by ideXlab platform
Sophie Grivaux - One of the best experts on this subject based on the ideXlab platform.
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Escaping a Neighborhood Along a Prescribed Sequence in Lie Groups and Banach Algebras
Canadian Mathematical Bulletin, 2019Co-Authors: Catalin Badea, Vincent Devinck, Sophie GrivauxAbstract:AbstractIt is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or Normed Algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Normed Algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved.
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Escaping a neighborhood along a prescribed sequence in Lie groups and Banach Algebras
arXiv: Functional Analysis, 2019Co-Authors: Catalin Badea, Vincent Devinck, Sophie GrivauxAbstract:It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux ([C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793]), arise naturally in the study of topological groups with no small subgroups, of Banach or Normed Algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Normed Algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given and other related results are proved.
Catalin Badea - One of the best experts on this subject based on the ideXlab platform.
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Escaping a Neighborhood Along a Prescribed Sequence in Lie Groups and Banach Algebras
Canadian Mathematical Bulletin, 2019Co-Authors: Catalin Badea, Vincent Devinck, Sophie GrivauxAbstract:AbstractIt is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or Normed Algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Normed Algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved.
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Escaping a neighborhood along a prescribed sequence in Lie groups and Banach Algebras
arXiv: Functional Analysis, 2019Co-Authors: Catalin Badea, Vincent Devinck, Sophie GrivauxAbstract:It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux ([C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793]), arise naturally in the study of topological groups with no small subgroups, of Banach or Normed Algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Normed Algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given and other related results are proved.
Camillo Trapani - One of the best experts on this subject based on the ideXlab platform.
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Locally convex quasi $C^*$-Normed Algebras
arXiv: Mathematical Physics, 2012Co-Authors: Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TrapaniAbstract:If $\ca_0[|\cdot|_0]$ is a $\cs$-Normed Algebra and $\tau$ a locally convex topology on $\ca_0$ making its multiplication separately continuous, then $\widetilde{\ca_0}[\tau]$ (completion of $\ca_0[\tau]$) is a locally convex quasi *-Algebra over $\ca_0$, but it is not necessarily a locally convex quasi *-Algebra over the $\cs$-Algebra $\widetilde{\ca_0}[|\cdot|_0]$ (completion of $\ca_0[|\cdot|_0]$). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi $\cs$-Normed Algebra, aiming at the investigation of $\widetilde{\ca_0}[\tau]$; in particular, we study its structure, *-representation theory and functional calculus.
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locally convex quasi c Normed Algebras
arXiv: Mathematical Physics, 2012Co-Authors: Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TrapaniAbstract:If $\ca_0[|\cdot|_0]$ is a $\cs$-Normed Algebra and $\tau$ a locally convex topology on $\ca_0$ making its multiplication separately continuous, then $\widetilde{\ca_0}[\tau]$ (completion of $\ca_0[\tau]$) is a locally convex quasi *-Algebra over $\ca_0$, but it is not necessarily a locally convex quasi *-Algebra over the $\cs$-Algebra $\widetilde{\ca_0}[|\cdot|_0]$ (completion of $\ca_0[|\cdot|_0]$). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi $\cs$-Normed Algebra, aiming at the investigation of $\widetilde{\ca_0}[\tau]$; in particular, we study its structure, *-representation theory and functional calculus.
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locally convex quasi c Normed Algebras
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TrapaniAbstract:Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -Normed Algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-Algebra over A 0 , but it is not necessarily a locally convex quasi ∗-Algebra over the C ∗ -Algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -Normed Algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.
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Locally convex quasi C∗-Normed Algebras
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Fabio Bagarello, Maria Fragoulopoulou, Atsushi Inoue, Camillo TrapaniAbstract:Abstract If A 0 [ ‖ ⋅ ‖ 0 ] is a C ∗ -Normed Algebra and τ a locally convex topology on A 0 making its multiplication separately continuous, then A 0 ˜ [ τ ] (completion of A 0 [ τ ] ) is a locally convex quasi ∗-Algebra over A 0 , but it is not necessarily a locally convex quasi ∗-Algebra over the C ∗ -Algebra A 0 ˜ [ ‖ ⋅ ‖ 0 ] (completion of A 0 [ ‖ ⋅ ‖ 0 ] ). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C ∗ -Normed Algebra, aiming at the investigation of A 0 ˜ [ τ ] ; in particular, we study its structure, ∗-representation theory and functional calculus.
Sam Morley - One of the best experts on this subject based on the ideXlab platform.
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The chain rule for F-differentiation
2016Co-Authors: T. Chaobankoh, Joel Feinstein, Sam MorleyAbstract:Let X be a perfect, compact subset of the complex plane, and let D (1)(X) denote the (complex) Algebra of continuously complex-differentiable functions on X. Then D(1)(X) is a Normed Algebra of functions but, in some cases, fails to be a Banach function Algebra. Bland and the second author investigated the completion of the Algebra D(1)(X), for certain sets X and collections F of paths in X, by considering F-differentiable functions on X. In this paper, we investigate composition, the chain rule, and the quotient rule for this notion of differentiability. We give an example where the chain rule fails, and give a number of sufficient conditions for the chain rule to hold. Where the chain rule holds, we observe that the Fa a di Bruno formula for higher derivatives is valid, and this allows us to give some results on homomorphisms between certain Algebras of F-differentiable functions.
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Homomorphisms between Algebras of $\mathcal F$-differentiable functions
arXiv: Functional Analysis, 2015Co-Authors: T. Chaobankoh, Joel Feinstein, Sam MorleyAbstract:Let $X$ be a perfect, compact subset of the complex plane, and let $D^{(1)}(X)$ denote the (complex) Algebra of continuously complex-differentiable functions on $X$. Then $D^{(1)}(X)$ is a Normed Algebra of functions but, in some cases, fails to be a Banach function Algebra. Bland and the second author investigated the completion of the Algebra $D^{(1)}(X)$, for certain sets $X$ and collections $\mathcal{F}$ of paths in $X$, by considering $\mathcal{F}$-differentiable functions on $X$. In this paper, we investigate composition, the chain rule, and the quotient rule for this notion of differentiability. We also investigate homomorphisms between certain Algebras of $\mathcal{F}$-differentiable functions.
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The chain rule for $\mathcal F$-differentiation
arXiv: Functional Analysis, 2015Co-Authors: T. Chaobankoh, Joel Feinstein, Sam MorleyAbstract:Let $X$ be a perfect, compact subset of the complex plane, and let $D^{(1)}(X)$ denote the (complex) Algebra of continuously complex-differentiable functions on $X$. Then $D^{(1)}(X)$ is a Normed Algebra of functions but, in some cases, fails to be a Banach function Algebra. Bland and the second author investigated the completion of the Algebra $D^{(1)}(X)$, for certain sets $X$ and collections $\mathcal{F}$ of paths in $X$, by considering $\mathcal{F}$-differentiable functions on $X$. In this paper, we investigate composition, the chain rule, and the quotient rule for this notion of differentiability. We give an example where the chain rule fails, and give a number of sufficient conditions for the chain rule to hold. Where the chain rule holds, we observe that the Fa\'a di Bruno formula for higher derivatives is valid, and this allows us to give some results on homomorphisms between certain Algebras of $\mathcal{F}$-differentiable functions.
Vincent Devinck - One of the best experts on this subject based on the ideXlab platform.
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Escaping a Neighborhood Along a Prescribed Sequence in Lie Groups and Banach Algebras
Canadian Mathematical Bulletin, 2019Co-Authors: Catalin Badea, Vincent Devinck, Sophie GrivauxAbstract:AbstractIt is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or Normed Algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Normed Algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved.
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Escaping a neighborhood along a prescribed sequence in Lie groups and Banach Algebras
arXiv: Functional Analysis, 2019Co-Authors: Catalin Badea, Vincent Devinck, Sophie GrivauxAbstract:It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux ([C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793]), arise naturally in the study of topological groups with no small subgroups, of Banach or Normed Algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Normed Algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given and other related results are proved.
