scholarly journals Weakly continuous functions on Banach spaces not containing $l\sb 1$

1993 ◽  
Vol 119 (1) ◽  
pp. 147-147
Author(s):  
Joaqu{í}n M. Guti{érrez
Keyword(s):  
Banach Spaces ◽  
Continuous Functions ◽  
Weakly Continuous

scholarly journals Function spaces and the Mosco topology

1990 ◽  
Vol 42 (1) ◽  
pp. 7-19 ◽  
Author(s):  
Gerald Beer ◽  
Robert Tamaki
Keyword(s):  
Banach Spaces ◽  
Function Space ◽  
Weak Topology ◽  
Continuous Functions ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Compact Open Topology ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Weakly Continuous

Let X and Y be Banach spaces and let C(X, Y) be the functions from X to Y continuous with respect to the weak topology on X and the strong topology on Y. By the Mosco topology τM on C(X, Y) we mean the supremum of the Fell topologies determined by the weak and strong topologies on X × Y, where functions are identified with their graphs. The function space is Hausdorff if and only if both X and Y are reflexive. Moreover, τM coincides with the stronger compact-open topology on C(X, Y) provided X is reflexive and Y is finite dimensional. We also show convergence in either sense is properly weaker than continuous convergence, even for continuous linear functionals, whenever X is infinite dimensional. For real-valued weakly continuous functions, τM is the supremum of the Mosco epitopology and the Mosco hypotopology if and only if X is reflexive.

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 A note on weakly θ-continuous functions

1989 ◽  
Vol 12 (1) ◽  
pp. 9-13 ◽  
Author(s):  
M. Mrševic ◽  
I. L. Reilly
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
New Class ◽  
Weakly Continuous ◽  
Class Of Functions

Recently a new class of functions between topological spaces, called weaklyθ-continuous functions, has been introduced and studied. In this paper we show how an appropriate change of topology on the domain of a weaklyθ-continuous function reduces it to a weakly continuous function. This paper examines some of the consequences of this result.

ON ALMOST WEAKLY CONTINUOUS FUNCTIONS

1998 ◽  
Vol 31 (2) ◽  
Author(s):  
Saeid Jafari ◽  
Takashi Noiri
Keyword(s):  
Continuous Functions ◽  
Weakly Continuous

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
Sign in / Sign up

Export Citation Format

Share Document