Abstract. Generalizing Pisier’s idea, we introduce a Hilbertian matrix cross normed space associated with a pair of symmetric normed ideals. When the two ideals coincide, we show that our construction gives an operator space if and only if the ideal is the Schatten class. In general, a pair of symmetric normed ideals that are not necessarily the Schatten class may give rise to an operator space...

LetX be a complex Banach space andX∗ its dual space. We consider the topological subspace Π X { x, x∗ : x∗ x 1 ‖x‖ ‖x∗‖} of the product space BX ×BX∗ , equipped with norm and weak-∗ topology on the unit ball BX ofX and its dual unit ball BX∗ , respectively. It is easy to see that Π X is a closed subspace of BX × BX∗ . For two complex Banach spaces X and Y , denote by Cb BX : Y the Banach space ...

We study transitivity conditions on the norm of JB∗-triples, C∗-algebras, JBalgebras, and their preduals. We show that, for the predual X of a JBW∗-triple, each one of the following conditions i) and ii) implies that X is a Hilbert space. i) The closed unit ball of X has some extreme point and the norm of X is convex transitive. ii) The set of all extreme points of the closed unit ball of X is ...

In this paper, we will present several new results in finite and countable dimensional separable real Hilbert space phase retrieval norm by fusion frames. We characterize of for frames similar vectors show that only one direction holds vector case, every tight frame can do retrieval. Also the unitary operators preserve (norm) retrievability make a detailed study when hyperplanes general result ...

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...