Banach Spaces of Continuous Functions as Dual Spaces

2016 ◽  
Author(s):  
H. G. Dales ◽  
F.K. Dashiell, ◽  
A.T.-M. Lau ◽  
D. Strauss
Keyword(s):  
Banach Spaces ◽  
Continuous Functions ◽  
Dual Spaces ◽  
Spaces Of Continuous Functions

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.

Quotients of indecomposable Banach spaces of continuous functions

2012 ◽  
Vol 212 (3) ◽  
pp. 259-283 ◽  
Author(s):  
Rogério Augusto dos Santos Fajardo
Keyword(s):  
Banach Spaces ◽  
Continuous Functions ◽  
Spaces Of Continuous Functions
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