Translator Disclaimer
september 2022 Distinguished vector-valued continuous function spaces and injective tensor products
J. C. Ferrando, J. Ka̧kol
Bull. Belg. Math. Soc. Simon Stevin 28(5): 709-721 (september 2022). DOI: 10.36045/j.bbms.210812

Abstract

The paper continues the study on the distinguished property of the space $C_{p}\left( X\right) $ (of real-valued continuous functions over a Tychonoff space $X$ in the pointwise topology) under the formation of tensor products towards the following research directions: $\left( i\right) $ the injective tensor product $C_{p}\left( X\right) \otimes _{\varepsilon }E$ of $C_{p}\left( X\right) $ and a real locally convex space $E$ (and its completion $C_{p}\left( X\right) \,\widehat{\otimes }_{\varepsilon }\,E$), and $\left( ii\right) $ the space $C_{p}\left( X,E\right) $ of all $E$-valued continuous functions (with a normed space $E$) endowed with the pointwise topology. This work leads also to a new characterization of distinguished Fréchet locally convex spaces $E$. We show, e.g., that if $C_{p}(X)$ is metrizable, then $E$ is distinguished if and only if metrizable $C_{p}\left( X\right) \otimes _{\varepsilon }E$ is distinguished.

Citation

Download Citation

J. C. Ferrando. J. Ka̧kol. "Distinguished vector-valued continuous function spaces and injective tensor products." Bull. Belg. Math. Soc. Simon Stevin 28 (5) 709 - 721, september 2022. https://doi.org/10.36045/j.bbms.210812

Information

Published: september 2022
First available in Project Euclid: 16 September 2022

Digital Object Identifier: 10.36045/j.bbms.210812

Keywords: Distinguished space , Fréchet space‎ , injective and projective tensor product , nuclear space , vector-valued continuous function

Rights: Copyright © 2022 The Belgian Mathematical Society

JOURNAL ARTICLE
13 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.28 • No. 5 • september 2022
Back to Top