The Experts below are selected from a list of 51 Experts worldwide ranked by ideXlab platform
Dumitru Popa - One of the best experts on this subject based on the ideXlab platform.
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(r,p)-Absolutely Summing Operators on the space C (T,X) and applications
Hindawi Limited, 2001Co-Authors: Dumitru PopaAbstract:We give necessary and sufficient conditions for an Operator on the space C (T,X) to be (r,p)-Absolutely Summing. Also we prove that the injective tensor product of an integral Operator and an (r,p)-Absolutely Summing Operator is an (r,p)-Absolutely Summing Operator
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$(r,p)$-Absolutely Summing Operators on the space $C(T,X)$ and applications
Abstract and Applied Analysis, 2001Co-Authors: Dumitru PopaAbstract:We give necessary and sufficient conditions for an Operator on the space C (T,X) to be (r,p)-Absolutely Summing. Also we prove that the injective tensor product of an integral Operator and an (r,p)-Absolutely Summing Operator is an (r,p)-Absolutely Summing Operator.
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Positive Absolutely Summing Operators on the Köthe spaces
Positivity, 2001Co-Authors: Dumitru PopaAbstract:In this paper we characterize the positive Absolutely Summing Operators on the Kothe space E(X), with X a Banach lattice, extending a previous result. We prove that a composition Operator of two positive Absolutely Summing Operators is a positive Absolutely Summing Operator. An interpolation result for the positive Absolutely Summing Operators is obtained.
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2-Absolutely Summing Operators on the Space C(T, X)☆
Journal of Mathematical Analysis and Applications, 1999Co-Authors: Dumitru PopaAbstract:Abstract We give for some Banach spaces X and Y examples of linear and continuous Operators U: C(T, X) → Y, such that U#ϕ ∈ As2(X, Y), for each ϕ ∈ C(T) and U#: C(T) → As2(X, Y) is a 2-Absolutely Summing Operator with respect to the 2-absolute norm on As2(X, Y), but U is not 2-Absolutely Summing.
Narcisse Randrianantoanina - One of the best experts on this subject based on the ideXlab platform.
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Compact range property and Operators on C^*-algebras
Proceedings of the American Mathematical Society, 2000Co-Authors: Narcisse RandrianantoaninaAbstract:We prove that a Banach space E has the compact range property (CRP) if and only if, for any given C*-algebra A, every Absolutely Summing Operator from A into E is compact. Related results for p-Summing Operators (0 < p < 1) are also discussed as well as Operators on non-commutative Llspaces and C*-Summing Operators.
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Compact range property and Operators on $C^*$-algebras
arXiv: Functional Analysis, 2000Co-Authors: Narcisse RandrianantoaninaAbstract:We prove that a Banach space $E$ has the compact range property (CRP) if and only if for any given $C^*$-algebra $\cal A$, every Absolutely Summing Operator from $\cal A$ into $E$ is compact.
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Absolutely Summing Operators on non-commutative C ∗ -algebras and applications
1999Co-Authors: Narcisse RandrianantoaninaAbstract:Abstract. Let E be a Banach space that does not contain any copy of ℓ 1 and A be a non commutative C ∗-algebra. We prove that every Absolutely Summing Operator from A into E ∗ is compact, thus answering a question of Pe̷lczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additive A ∗-valued measure with bounded variation and whose Fourier transform is supported by Λ has relatively compact range. Extensions of the same result to symmetric spaces of measurable Operators are also presented. 1
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Factorization of Operators on $C^*$-algebras
arXiv: Functional Analysis, 1997Co-Authors: Narcisse RandrianantoaninaAbstract:Let $A$ be a $C^*$-algebra. It is shown that every Absolutely Summing Operator from $A$ into $\ell_2$ factors through a Hilbert space Operator that belongs to the 4-Schatten- von Neumann class. We also provide finite dimensinal examples that show that one can not improve the 4-Schatten-von Neumann class to $p$-Schatten von Neumann class for any $p 0$, the $\epsilon$-capacity of the image of the unit ball of $A$ under $T$ does not exceed $N(\epsilon)$. This aswers positively a question raised by Pe\l czynski.
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Absolutely Summing Operators on non commutative $C^*$-algebras and applications
arXiv: Functional Analysis, 1995Co-Authors: Narcisse Randrianantoanina, Vern I. PaulsenAbstract:Let E be a Banach space that does not contain any copy of ' 1 andA be a non commutative C -algebra. We prove that every Absolutely Summing Operator fromA into E is compact, thus answering a question of Pe lczy nski. As application, we show that if G is a compact metrizable abelian group and is a Riesz subset of its dual then every countably additive A -valued measure with bounded variation and whose Fourier transform is supported by has relatively compact range. Extensions of the same result to sym- metric spaces of measurable Operators are also presented.
José Rodríguez - One of the best experts on this subject based on the ideXlab platform.
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On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
Journal of Mathematical Analysis and Applications, 2008Co-Authors: José RodríguezAbstract:Abstract We show that McShane and Pettis integrability coincide for functions f : [ 0 , 1 ] → L 1 ( μ ) , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [ 0 , 1 ] → X and an Absolutely Summing Operator u from X to another Banach space Y such that the composition u ○ h : [ 0 , 1 ] → Y is not Bochner integrable; in particular, h is not McShane integrable.
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Absolutely Summing Operators and integration of vector-valued functions
Journal of Mathematical Analysis and Applications, 2006Co-Authors: José RodríguezAbstract:AbstractLet (Ω,Σ,μ) be a complete probability space and u:X→Y an Absolutely Summing Operator between Banach spaces. We prove that for each Dunford integrable (i.e., scalarly integrable) function f:Ω→X the composition u○f is scalarly equivalent to a Bochner integrable function. Such a composition is shown to be Bochner integrable in several cases, for instance, when f is properly measurable, Birkhoff integrable or McShane integrable, as well as when X is a subspace of an Asplund generated space or a subspace of a weakly Lindelöf space of the form C(K). We also study the continuity of the composition Operator f↦u○f. Some other applications are given
Randrianantoanina Narcisse - One of the best experts on this subject based on the ideXlab platform.
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Compact range property and Operators on $C^*$-algebras
2000Co-Authors: Randrianantoanina NarcisseAbstract:We prove that a Banach space $E$ has the compact range property (CRP) if and only if for any given $C^*$-algebra $\cal A$, every Absolutely Summing Operator from $\cal A$ into $E$ is compact.Comment: 8 page
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Absolutely Summing Operators on non commutative $C^*$-algebras and applications
1995Co-Authors: Randrianantoanina NarcisseAbstract:Let $E$ be a Banach space that does not contain any copy of $\ell^1$ and $\A$ be a non commutative $C^*$-algebra. We prove that every Absolutely Summing Operator from $\A$ into $E^*$ is compact, thus answering a question of Pe\l czynski. As application, we show that if $G$ is a compact metrizable abelian group and $\Lambda$ is a Riesz subset of its dual then every countably additive $\A^*$-valued measure with bounded variation and whose Fourier transform is supported by $\Lambda$ has relatively compact range. Extensions of the same result to symmetric spaces of measurable Operators are also presented
Popa Dumitru - One of the best experts on this subject based on the ideXlab platform.
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2-Absolutely Summing Operators on the Space C(T,X)
Academic Press., 1999Co-Authors: Popa DumitruAbstract:AbstractWe give for some Banach spaces X and Y examples of linear and continuous Operators U: C(T,X)→Y, such that U#ϕ∈As2(X,Y), for each ϕ∈C(T) and U#: C(T)→As2(X,Y) is a 2-Absolutely Summing Operator with respect to the 2-absolute norm on As2(X,Y), but U is not 2-Absolutely Summing