scholarly journals The weakly compact approximation of the projective tensor product of Banach spaces

2012 ◽  
Vol 37 ◽  
pp. 461-465 ◽  
Author(s):  
Qingying Bu
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Weakly Compact ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Compact Approximation

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.

scholarly journals Types of Radon-Nikodym properties for the projective tensor product of Banach spaces

2003 ◽  
Vol 47 (4) ◽  
pp. 1303-1326 ◽  
Author(s):  
Qingying Bu ◽  
Joe Diestel ◽  
Patrick Dowling ◽  
Eve Oja
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor

scholarly journals Weakly open sets in the unit ball of the projective tensor product of Banach spaces

2011 ◽  
Vol 383 (2) ◽  
pp. 461-473 ◽  
Author(s):  
María D. Acosta ◽  
Julio Becerra Guerrero ◽  
Angel Rodríguez-Palacios
Keyword(s):  
Tensor Product ◽  
Unit Ball ◽  
Banach Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor

scholarly journals Polynomial Grothendieck properties

1995 ◽  
Vol 37 (2) ◽  
pp. 211-219 ◽  
Author(s):  
Manuel González ◽  
Joaquí M. Gutiérrez
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Homogeneous Polynomial ◽  
Bounded Operator ◽  
Weakly Compact ◽  
Completely Continuous ◽  
Projective Tensor Product ◽  
Linear Bounded Operator ◽  
Grothendieck Property ◽  
Projective Tensor

AbstractA Banach space sE has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space (kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric A>fold projective tensor product of £(i.e., the predual of (kE)) having the Grothendieck property. The Grothendieck property of the projective tensor product EF is also characterized. Moreover, the Grothendieck property of E is described in terms of sequences of polynomials. Finally, it is shown that if every operator from E into c0 is completely continuous, then so is every polynomial between these spaces.

A New Approach to Operator Spaces

1991 ◽  
Vol 34 (3) ◽  
pp. 329-337 ◽  
Author(s):  
Edward G. Effros ◽  
Zhong-Jin Ruan
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Operator Space ◽  
Operator Spaces ◽  
New Approach ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Space Concepts ◽  
Injective Operator

AbstractThe authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space.

scholarly journals EMBEDDING $\ell_1$ INTO THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES

2007 ◽  
Vol 11 (4) ◽  
pp. 1119-1125
Author(s):  
Xiaoping Xue ◽  
Yongjin Li ◽  
Qingying Bu
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor
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