Displaying similar documents to “On the structure of tensor norms related to (p,σ)-absolutely continuous operators.”

On operator ideals related to (p,σ)-absolutely continuous operators

J. López Molina, E. Sánchez Pérez (2000)

Studia Mathematica

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We study tensor norms and operator ideals related to the ideal P p , σ , 1 < p < ∞, 0 < σ < 1, of (p,σ)-absolutely continuous operators of Matter. If α is the tensor norm associated with P p , σ (in the sense of Defant and Floret), we characterize the ( α ' ) t -nuclear and ( α ' ) t - integral operators by factorizations by means of the composition of the inclusion map L r ( μ ) → L 1 ( μ ) + L p ( μ ) with a diagonal operator B w : L ∞ ( μ ) → L r ( μ ) , where r is the conjugate exponent of p’/(1-σ). As an application we study the reflexivity of the components...

Localization of bounded sets in tensor products.

A. Peris, M. J. Rivera (1996)

Revista Matemática de la Universidad Complutense de Madrid

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The problem of topologies of Grothendieck is considered for complete tensor products of Fréchet spaces endowed with the topology defined by an arbitrary tensor norm. Some consequences on the stability of certain locally convex properties in spaces of operators are also given.

Isomorphism of some anisotropic Besov and sequence spaces

A. Kamont (1994)

Studia Mathematica

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An isomorphism between some anisotropic Besov and sequence spaces is established, and the continuity of a Stieltjes-type integral operator, acting on some of these spaces, is proved.

Clarkson type inequalities and their relations to the concepts of type and cotype.

Mikio Kato, Lars-Erik. Persson, Yasuji Takahashi (2000)

Collectanea Mathematica

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We prove some multi-dimensional Clarkson type inequalities for Banach spaces. The exact relations between such inequalities and the concepts of type and cotype are shown, which gives a conclusion in an extended setting to M. Milman's observation on Clarkson's inequalities and type. A similar investigation conceming the close connection between random Clarkson inequality and the corresponding concepts of type and cotype is also included. The obtained results complement, unify and generalize...