Characterization of barrelled, d-barrelled, and m?-barrelled spaces of continuous functions

1985 ◽  
Vol 37 (5) ◽  
pp. 418-420
Author(s):  
I. I. Perepechai
Keyword(s):  
Continuous Functions ◽  
Spaces Of Continuous Functions ◽  
Barrelled Spaces

scholarly journals Convolution operators on weighted spaces of continuous functions and supremal convolution

2019 ◽  
Vol 199 (4) ◽  
pp. 1547-1569
Author(s):  
T. Kleiner ◽  
R. Hilfer
Keyword(s):  
Continuous Functions ◽  
Weighted Spaces ◽  
Constructive Method ◽  
Convolution Operators ◽  
Linear Combinations ◽  
The Third ◽  
Bounded Set ◽  
Spaces Of Continuous Functions ◽  
Bounded Sets

AbstractThe convolution of two weighted balls of measures is proved to be contained in a third weighted ball if and only if the supremal convolution of the corresponding two weights is less than or equal to the third weight. Here supremal convolution is introduced as a type of convolution in which integration is replaced with supremum formation. Invoking duality the equivalence implies a characterization of equicontinuity of weight-bounded sets of convolution operators having weighted spaces of continuous functions as domain and range. The overall result is a constructive method to define weighted spaces on which a given set of convolution operators acts as an equicontinuous family of endomorphisms. The result is applied to linear combinations of fractional Weyl integrals and derivatives with orders and coefficients from a given bounded set.

scholarly journals Uniformly summing sets of operators on spaces of continuous functions

2004 ◽  
Vol 2004 (63) ◽  
pp. 3397-3407
Author(s):  
J. M. Delgado ◽  
Cándido Piñeiro
Keyword(s):  
Banach Spaces ◽  
Continuous Functions ◽  
General Properties ◽  
Spaces Of Continuous Functions ◽  
Uniformly Convergent

LetXandYbe Banach spaces. A setℳof 1-summing operators fromXintoYis said to beuniformly summingif the following holds: given a weakly 1-summing sequence(xn)inX, the series∑n‖Txn‖is uniformly convergent inT∈ℳ. We study some general properties and obtain a characterization of these sets whenℳis a set of operators defined on 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.

scholarly journals BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY

2007 ◽  
Vol 49 (1) ◽  
pp. 145-154
Author(s):  
BRUCE A. BARNES
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Integral Operators ◽  
Continuous Functions ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Closed Range ◽  
Bounded Linear ◽  
Spaces Of Continuous Functions

Abstract.LetTbe a bounded linear operator on a Banach spaceW, assumeWandYare in normed duality, and assume thatThas adjointT†relative toY. In this paper, conditions are given that imply that for all λ≠0, λ−Tand λ −T†maintain important standard operator relationships. For example, under the conditions given, λ −Thas closed range if, and only if, λ −T†has closed range.These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.

scholarly journals A Characterization of the Existence of a Fundamental Bounded Resolution for the Space Cc(X) in Terms of X

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Juan Carlos Ferrando
Keyword(s):  
Continuous Functions ◽  
Compact Open Topology ◽  
Tychonoff Space ◽  
Bounded Sets

We characterize in terms of the topology of a Tychonoff space X the existence of a bounded resolution for CcX that swallows the bounded sets, where CcX is the space of real-valued continuous functions on X equipped with the compact-open topology.

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