Multiplication Operators on Generalized Weighted Spaces of Continuous Functions
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- 作者：Mohammed Klilou ; Lahbib Oubbi
- 关键词：Generalized weighted spaces of continuous functions ; Multiplication operators
- 刊名：Mediterranean Journal of Mathematics
- 出版年：2016
- 出版时间：October 2016
- 年：2016
- 卷：13
- 期：5
- 页码：3265-3280
- 全文大小：568 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Birkh盲user Basel
- ISSN：1660-5454
- 卷排序：13
文摘
We deal with the generalized weighted spaces \({CV(X, H)}\) and \({CV_{0}(X, H)}\) of continuous functions associated with a Nachbin family \({V}\) consisting of strongly upper semi-continuous (u.s.c. in short) functions from a completely regular Hausdorff space \({X}\) into the set \({B^{+}(H)}\) of positive operators on a Hilbert space \({H}\). We first propose an adequate framework to conduct a reasonable study on such spaces and thus clarify a certain ambiguity in the literature. We then give the conditions under which such spaces are complete. Necessary and sufficient conditions for a subspace of \({CV_{0}(X, H),}\) which is a \({C_{b}(X)}\)-module to be dense, are also obtained. Furthermore, for any continuous \({B(H)}\)-valued mapping \({\varphi}\) on \({X}\), we give necessary and sufficient conditions for the multiplication operator \({M_{\varphi}}\) induced by φ to be continuous, bounded below, invertible or having a dense range.