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Absolutely Summing Operator
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.

(r,p)Absolutely Summing Operators on the space C (T,X) and applications
Hindawi Limited, 2001CoAuthors: 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

$(r,p)$Absolutely Summing Operators on the space $C(T,X)$ and applications
Abstract and Applied Analysis, 2001CoAuthors: 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.

Positive Absolutely Summing Operators on the Köthe spaces
Positivity, 2001CoAuthors: 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.
Narcisse Randrianantoanina – One of the best experts on this subject based on the ideXlab platform.

Compact range property and Operators on C^*algebras
Proceedings of the American Mathematical Society, 2000CoAuthors: 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 pSumming Operators (0 < p < 1) are also discussed as well as Operators on noncommutative Llspaces and C*Summing Operators.

Compact range property and Operators on $C^*$algebras
arXiv: Functional Analysis, 2000CoAuthors: 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.

Absolutely Summing Operators on noncommutative C ∗ algebras and applications
, 1999CoAuthors: 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
José Rodríguez – One of the best experts on this subject based on the ideXlab platform.

On the equivalence of McShane and Pettis integrability in nonseparable Banach spaces
Journal of Mathematical Analysis and Applications, 2008CoAuthors: 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.

Absolutely Summing Operators and integration of vectorvalued functions
Journal of Mathematical Analysis and Applications, 2006CoAuthors: 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 inteintegrable 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.

Compact range property and Operators on $C^*$algebras
, 2000CoAuthors: 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

Absolutely Summing Operators on non commutative $C^*$algebras and applications
, 1995CoAuthors: 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.

2Absolutely Summing Operators on the Space C(T,X)
Academic Press., 1999CoAuthors: 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 2Absolutely Summing Operator with respect to the 2absolute norm on As2(X,Y), but U is not 2Absolutely Summing