Titlebook: Introduction to Tensor Products of Banach Spaces; Raymond A. Ryan Book 2002 Springer-Verlag London 2002 Banach Space.Tensor Products.appro

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The Projective Tensor Product,near mappings just as the algebraic tensor product linearizes bilinear mappings. The projective tensor product derives its name from the fact that it behaves well with respect to quotient space constructions. The projective tensor product of ℓ. with . gives a representation of the space of absolutel

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The Injective Tensor Product,ctor valued functions and injective tensor products with ..(.) spaces provide an introduction to the Pettis integral. The duality theory of injective tensor products leads to the introduction of the important classes of integral bilinear forms and operators.

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The Approximation Property,ing issues concerning projective and injective tensor products. We then consider the following question: when are the projective or injective tensor products of reflexive spaces themselves reflexive? A satisfactory answer requires the use of the approximation property. Finally, we study tensor produ

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,The Radon-Nikodým Property,a Banach space. Those spaces for which the classical Radon—Nikodým Theorem extends to vector valued measures are said to have the Radon—Nikodým property. The identification of injective and projective tensor products of spaces of scalar measures in terms of spaces of vector measures sheds some light

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The Chevet-Saphar Tensor Products,tion of a tensor norm. We then investigate the Chevet-Saphar tensor norms, .. and ... The dual spaces of the corresponding tensor products lead us to the definition of the .-summing operators. We conclude with the fundamental Grothendieck Inequality and some of its applications.

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