Tensor Products of Non-Archimedean Weighted Spaces of Continuous Functions

1999 ◽  
Vol 6 (1) ◽  
pp. 33-44 ◽  
Author(s):  
A. K. Katsaras ◽  
A. Beloyiannis
Keyword(s):  
Tensor Product ◽  
Weighted Space ◽  
Tensor Products ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Spaces Of Continuous Functions

Abstract It is shown that the completion of the tensor product of two non-Archimedean weighted spaces of continuous functions is topologically isomorphic to another weighted space. Several applications of this result are given.

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 On weighted spaces without a fundamental sequence of bounded sets

2002 ◽  
Vol 30 (8) ◽  
pp. 449-457 ◽  
Author(s):  
J. O. Olaleru
Keyword(s):  
Weighted Space ◽  
General Setting ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Fundamental Sequence ◽  
Spaces Of Continuous Functions ◽  
Bounded Sets

The problem of countably quasi-barrelledness of weighted spaces of continuous functions, of which there are no results in the general setting of weighted spaces, is tackled in this paper. This leads to the study of quasi-barrelledness of weighted spaces in which, unlike that of Ernst and Schnettler (1986), though with a similar approach, we drop the assumption that the weighted space has a fundamental sequence of bounded sets. The study of countably quasi-barrelledness of weighted spaces naturally leads to definite results on the weighted (DF)-spaces for those weighted spaces with a fundamental sequence of bounded sets.

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 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 Tensor products of function algebras

1987 ◽  
Vol 36 (3) ◽  
pp. 417-423 ◽  
Author(s):  
Athanasios Kyriazis
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Continuous Functions ◽  
Compact Open Topology ◽  
Function Algebras ◽  
Fibre Product

For appropriate topclogical spaces X, Y, Z the algebra Cc(X xZY) of ℂ-valued continuous functions on the fibre product X xZY in the compact-open topology, describes the completed biprojective Cc(Z)-tensor product of Cc(X), Cc(Y).

A class of linear positive operators in weighted spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Ayşegül Erençin ◽  
H. Gül İnce ◽  
Ali Olgun
Keyword(s):  
Differential Equation ◽  
Continuous Functions ◽  
Positive Operators ◽  
Weighted Spaces ◽  
Convergence Properties ◽  
Linear Positive Operators ◽  
Spaces Of Continuous Functions

AbstractIn this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder.

Sign in / Sign up

Export Citation Format

Share Document