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Caractérisation Des Espaces 1-Matriciellement Normés

Le Merdy, Christian, Mezrag, Lahcéne (2002)

Serdica Mathematical Journal

Let X be a closed subspace of B(H) for some Hilbert space H. In [9], Pisier introduced Sp [X] (1 ≤ p ≤ +∞) by setting Sp [X] = (S∞ [X] , S1 [X])θ , (where θ =1/p , S∞ [X] = S∞ ⊗min X and S1 [X] = S1 ⊗∧ X) and showed that there are p−matricially normed spaces. In this paper we prove that conversely, if X is a p−matricially normed space with p = 1, then there is an operator structure on X, such that M1,n (X) = S1 [X] where Sn,1 [X] is the finite dimentional version of S1 [X]. For p...

Characterization of strict C*-algebras

O. Aristov (1994)

Studia Mathematica

A Banach algebra A is called strict if the product morphism is continuous with respect to the weak norm in A ⊗ A. The following result is proved: A C*-algebra is strict if and only if all its irreducible representations are finite-dimensional and their dimensions are bounded.

Coincidence of topologies on tensor products of Köthe echelon spaces

J. Bonet, A. Defant, A. Peris, M. Ramanujan (1994)

Studia Mathematica

We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from l p to l q . Several sharp forms of this result are also included.

Complementation in spaces of symmetric tensor products and polynomials.

Fernando Blasco (1996)

Extracta Mathematicae

Our aim here is to announce some properties of complementation for spaces of symmetric tensor products and homogeneous continuous polynomials on a locally convex space E that have, in particular, consequences in the study of the property (BB)n,s recently introduced by Dineen [8].

Complexification of the projective and injective tensor products

Gusti van Zyl (2008)

Studia Mathematica

We show that the Taylor (resp. Bochnak) complexification of the injective (projective) tensor product of any two real Banach spaces is isometrically isomorphic to the injective (projective) tensor product of the Taylor (Bochnak) complexifications of the two spaces.

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