Quojections and projective tensor products

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

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

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 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

scholarly journals Banach space sequences and projective tensor products

2003 ◽  
Vol 277 (2) ◽  
pp. 629-644 ◽  
Author(s):  
Jan H. Fourie ◽  
Ilse M. Röntgen
Keyword(s):  
Banach Space ◽  
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.

scholarly journals On the interpolation of injective or projective tensor products of Banach spaces

1991 ◽  
Vol 96 (1) ◽  
pp. 38-61 ◽  
Author(s):  
Omran Kouba
Keyword(s):  
Banach Spaces ◽  
Tensor Products ◽  
Projective Tensor

scholarly journals Locally decodable codes and the failure of cotype for projective tensor products

2012 ◽  
Vol 19 (0) ◽  
pp. 120-130 ◽  
Author(s):  
Oded Regev ◽  
Assaf Naor ◽  
Jop Briët
Keyword(s):  
Tensor Products ◽  
Projective Tensor ◽  
Locally Decodable Codes ◽  
Locally Decodable
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