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Factorization of operators on C*-algebras

Narcisse Randrianantoanina (1998)

Studia Mathematica

Let A be a C*-algebra. We prove that every absolutely summing operator from A into 2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and T Π 1 ( A , 2 ) with π 1 ( T ) 1 , then for every ε >0, the ε-capacity of...

Finite rank approximation and semidiscreteness for linear operators

Christian Le Merdy (1999)

Annales de l'institut Fourier

Given a completely bounded map u : Z M from an operator space Z into a von Neumann algebra (or merely a unital dual algebra) M , we define u to be C -semidiscrete if for any operator algebra A , the tensor operator I A u is bounded from A min Z into A nor M , with norm less than C . We investigate this property and characterize it by suitable approximation properties, thus generalizing the Choi-Effros characterization of semidiscrete von Neumann algebras. Our work is an extension of some recent work of Pisier on an analogous...

Finite rank operators in Jacobson radical 𝒩

Zhe Dong (2006)

Czechoslovak Mathematical Journal

In this paper we investigate finite rank operators in the Jacobson radical 𝒩 of A l g ( 𝒩 ) , where 𝒩 , are nests. Based on the concrete characterizations of rank one operators in A l g ( 𝒩 ) and 𝒩 , we obtain that each finite rank operator in 𝒩 can be written as a finite sum of rank one operators in 𝒩 and the weak closure of 𝒩 equals A l g ( 𝒩 ) if and only if at least one of 𝒩 , is continuous.

Finite sections of truncated Toeplitz operators

Steffen Roch (2015)

Concrete Operators

We describe the C*-algebra associated with the finite sections discretization of truncated Toeplitz operators on the model space K2u where u is an infinite Blaschke product. As consequences, we get a stability criterion for the finite sections discretization and results on spectral and pseudospectral approximation.

First results on spectrally bounded operators

M. Mathieu, G. J. Schick (2002)

Studia Mathematica

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E, where r(·) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.

Fréchet interpolation spaces and Grothendieck operator ideals.

Jesús M. Fernández Castillo (1991)

Collectanea Mathematica

Starting with a continuous injection I: X → Y between Banach spaces, we are interested in the Fréchet (non Banach) space obtained as the reduced projective limit of the real interpolation spaces. We study relationships among the pertenence of I to an operator ideal and the pertenence of the given interpolation space to the Grothendieck class generated by that ideal.

Fully representable and *-semisimple topological partial *-algebras

J.-P. Antoine, G. Bellomonte, C. Trapani (2012)

Studia Mathematica

We continue our study of topological partial *-algebras, focusing our attention on *-semisimple partial *-algebras, that is, those that possess a multiplication core and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals, and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the aim of characterizing a *-semisimple partial...

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