A Characterization of the Normed Vector Ordered Spaces of Continuous Functions Over a Compact Space

1949 ◽  
Vol 71 (3) ◽  
pp. 701 ◽  
Author(s):  
Leopoldo Nachbin
Keyword(s):  
Compact Space ◽  
Continuous Functions ◽  
Spaces Of Continuous Functions ◽  
Normed Vector

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 On -Cogenerated Commutative Unital -Algebras

Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Ehsan Momtahan
Keyword(s):  
Compact Space ◽  
Commutative Algebra ◽  
Cardinal Number ◽  
Continuous Functions ◽  
Regular Space ◽  
Completely Regular ◽  
Simple Characterization ◽  
Maximal Ideals ◽  
Complex Valued

Gelfand-Naimark's theorem states that every commutative -algebra is isomorphic to a complex valued algebra of continuous functions over a suitable compact space. We observe that for a completely regular space , is dense--separable if and only if is -cogenerated if and only if every family of maximal ideals of with zero intersection has a subfamily with cardinal number less than and zero intersection. This gives a simple characterization of -cogenerated commutative unital -algebras via their maximal ideals.

LΣ(≤ ω)-spaces and spaces of continuous functions

2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Israel Lara ◽  
Oleg Okunev
Keyword(s):  
Compact Space ◽  
Pointwise Convergence ◽  
Continuous Functions ◽  
Spaces Of Continuous Functions ◽  
Topology Of Pointwise Convergence

AbstractWe present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $$ \mathfrak{c} $$ is an LΣ(≤ ω)-space.

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.

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