Polynomial properties and symmetric tensor product of Banach spaces

2000 ◽  
Vol 74 (1) ◽  
pp. 40-49 ◽  
Author(s):  
F. Bombal ◽  
M. Fernández
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Symmetric Tensor ◽  
Symmetric Tensor Product

scholarly journals DAUGAVET PROPERTY IN TENSOR PRODUCT SPACES

2019 ◽  
pp. 1-20 ◽  
Author(s):  
Abraham Rueda Zoca ◽  
Pedro Tradacete ◽  
Ignacio Villanueva
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Tensor Products ◽  
Symmetric Tensor ◽  
Continuous Functions ◽  
Product Spaces ◽  
Projective Tensor ◽  
Spaces Of Continuous Functions ◽  
Daugavet Property

We study the Daugavet property in tensor products of Banach spaces. We show that $L_{1}(\unicode[STIX]{x1D707})\widehat{\otimes }_{\unicode[STIX]{x1D700}}L_{1}(\unicode[STIX]{x1D708})$ has the Daugavet property when $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D708}$ are purely non-atomic measures. Also, we show that $X\widehat{\otimes }_{\unicode[STIX]{x1D70B}}Y$ has the Daugavet property provided $X$ and $Y$ are $L_{1}$ -preduals with the Daugavet property, in particular, spaces of continuous functions with this property. With the same techniques, we also obtain consequences about roughness in projective tensor products as well as the Daugavet property of projective symmetric tensor products.

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

Some Properties of the Injective Tensor Product of Banach Spaces

2007 ◽  
Vol 23 (9) ◽  
pp. 1697-1706
Author(s):  
Xiao Ping Xue ◽  
Yong Jin Li ◽  
Qing Ying Bu
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Injective Tensor Product

Solutions of Certain Fractional Partial Differential Equations

2021 ◽  
Vol 20 ◽  
pp. 504-507
Author(s):  
Alsauodi Maha ◽  
Alhorani Mohammed ◽  
Khalil Roshdi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Tensor Product ◽  
Banach Spaces ◽  
Separation Of Variables ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

In this paper we find certain solutions of some fractional partial differential equations. Tensor product of Banach spaces is used where separation of variables does not work.

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
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