scholarly journals On the projection constants of some topological spaces and some applications

2001 ◽  
Vol 6 (5) ◽  
pp. 299-308 ◽  
Author(s):  
Entisarat El-Shobaky ◽  
Sahar Mohammed Ali ◽  
Wataru Takahashi
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Topological Spaces ◽  
Projective Tensor Product ◽  
Injective Tensor Product ◽  
Lower Estimation ◽  
Projective Tensor ◽  
Projection Constant

We find a lower estimation for the projection constant of the projective tensor productX⊗ ∧Yand the injective tensor productX⊗ ∨Y, we apply this estimation on some previous results, and we also introduce a new concept of the projection constants of operators rather than that defined for Banach spaces.

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

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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