On Kalton’s theorem for regular compact operators and Grothendieck property for positive projective tensor products

2020 ◽  
Vol 148 (6) ◽  
pp. 2459-2467
Author(s):  
Qingying Bu
Keyword(s):  
Tensor Products ◽  
Compact Operators ◽  
Grothendieck Property ◽  
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

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

Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-II

2009 ◽  
Vol 32 (3) ◽  
pp. 339-350 ◽  
Author(s):  
Qingying Bu∗ ◽  
Michelle Craddock ◽  
Donghai Ji
Keyword(s):  
Tensor Products ◽  
Banach Lattices ◽  
Grothendieck Property

Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I

Positivity ◽  
2009 ◽  
Vol 14 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Donghai Ji ◽  
Michelle Craddock ◽  
Qingying Bu
Keyword(s):  
Tensor Products ◽  
Banach Lattices ◽  
Grothendieck Property

Quojections and projective tensor products

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