A Study of Boundedness in Probabilistic Normed Spaces

Probabilistic normed spaces have been redefined by Alsina, Schweizer, and Sklar. We give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 1999-04, Vol.232 (1), p.183-196
Main Authors: Guillén, Bernardo Lafuerza, Lallena, José Antonio Rodrı́guez, Sempi, Carlo
Format: Article
Language:English
Subjects:
Exact sciences and technology
Functional analysis
General topics
Mathematical analysis
Mathematics
Operator theory
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
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Description
Summary:Probabilistic normed spaces have been redefined by Alsina, Schweizer, and Sklar. We give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1998.6261