The concept of orthogonality in normed linear spaces has been studied extensively by BIRKHOFF [3], JAMES IS], [7], [8], and the present authors [l], 151, among others. The most natural notion of orthogonality arises in the case where there is an inner product (-, -) compatible with the norm 11. 11 o
A Study of Boundedness in Probabilistic Normed Spaces
✍ Scribed by Bernardo Lafuerza Guillén; José Antonio Rodrı́guez Lallena; Carlo Sempi
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 104 KB
- Volume
- 232
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
A number of writers have defined a concept of angle in a normed linear space or metric space by means of the law of cosines, and have studied the properties of these angles obtaining, in some cases, characterizations of real inner product spaces. (For a summary of earlier results see MARTIN and VAL