Diagonals of projective tensor products and orthogonally additive polynomials

2014 ◽  
Vol 221 (2) ◽  
pp. 101-115 ◽  
Author(s):  
Qingying Bu ◽  
Gerard Buskes
Keyword(s):  
Tensor Products ◽  
Projective Tensor ◽  
Orthogonally Additive

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

scholarly journals SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS

2021 ◽  
pp. 1-14
Author(s):  
R.M. CAUSEY
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Tensor Products ◽  
Continuous Functions ◽  
Hausdorff Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Spaces Of Continuous Functions

Abstract Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

The classical subspaces of the projective tensor products of lpand C(α) spaces, α< ω1

2013 ◽  
Vol 214 (3) ◽  
pp. 237-250
Author(s):  
Elói Medina Galego ◽  
Christian Samuel
Keyword(s):  
Tensor Products ◽  
Projective Tensor

scholarly journals On the geometry of projective tensor products

2017 ◽  
Vol 273 (2) ◽  
pp. 471-495 ◽  
Author(s):  
Ohad Giladi ◽  
Joscha Prochno ◽  
Carsten Schütt ◽  
Nicole Tomczak-Jaegermann ◽  
Elisabeth Werner
Keyword(s):  
Tensor Products ◽  
Projective Tensor

Quojections and projective tensor products

1985 ◽  
Vol 45 (2) ◽  
pp. 169-173 ◽  
Author(s):  
Jos� Bonet
Keyword(s):  
Tensor Products ◽  
Projective Tensor

scholarly journals On the equality of injective and projective tensor products

1988 ◽  
Vol 38 (3) ◽  
pp. 464-472
Author(s):  
Hans Jarchow ◽  
Kamil John
Keyword(s):  
Tensor Products ◽  
Projective Tensor

scholarly journals Locally Convex Spaces with Toeplitz Decompositions

2000 ◽  
Vol 68 (1) ◽  
pp. 19-40
Author(s):  
Pedro J. Paúl ◽  
Carmen Sáez ◽  
Juan M. Virués
Keyword(s):  
Sufficient Conditions ◽  
Tensor Products ◽  
Schwartz Space ◽  
Locally Convex Spaces ◽  
Convex Structure ◽  
Toeplitz Decomposition ◽  
Projective Tensor ◽  
Finite Matrix ◽  
Montel Space ◽  
Locally Convex

AbstractA Toeplitz decomposition of a locally convez space E into subspaces (Ek) with continuous projections (Pk) is a decomposition of every x ∈ E as x = ΣkPkx where ordinary summability has been replaced by summability with respect to an infinite and row-finite matrix. We extend to the setting of Toeplitz decompositions a number of results about the locally convex structure of a space with a Schauder decomposition. Namely, we give some necessary or sufficient conditions for being reflexive, a Montel space or a Schwartz space. Roughly speaking, each of these locally convex properties is linked to a property of the convergence of the decomposition. We apply these results to study some structural questions in projective tensor products and spaces with Cesàro bases.

On the reciprocal Dunford-Pettis property in projective tensor products

1991 ◽  
Vol 109 (1) ◽  
pp. 161-166 ◽  
Author(s):  
G. Emmanuele
Keyword(s):  
Banach Space ◽  
Tensor Products ◽  
Projective Tensor

AbstractWe prove the following result: if a Banach space E does not contain l1 and F has the (RDPP), then E ⊗nF has the same property, provided that L(E, F*) = K(E, F*). Hence we prove that if E ⊗n F has the (RDPP) then at least one of the spaces E and F must not contain l1. Some corollaries are then presented as well as results concerning the necessity of the hypothesis L(E, F*) = K(E, F*).

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