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The Bishop-Phelps-Bollobas point propertyopen access
- Authors
- Dantas, Sheldon; Kim, Sun Kwang; Lee, Han Ju
- Issue Date
- 15-Dec-2016
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Bishop-Phelps theorem; Bishop-Phelps-Bollobas property; Norm attaining; Bilinear forms
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.444, no.2, pp 1739 - 1751
- Pages
- 13
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Volume
- 444
- Number
- 2
- Start Page
- 1739
- End Page
- 1751
- ISSN
- 0022-247X
1096-0813
- Abstract
- In this article, we study a version of the Bishop-Phelps-Bollobas property. We investigate a pair of Banach spaces (X, Y) such that every operator from X into Y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop-Phelps-Bollobas point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs (X, Y) which have and fail this property. Some stability results are obtained about l(1) and l(infinity) sums of Banach spaces and we also study this property for bilinear mappings. (C) 2016 Elsevier Inc. All rights reserved.
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)