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Weakening of a local Bollobás type property and geometry of Banach spaces.
- Source :
-
Acta Scientiarum Mathematicarum . May2024, Vol. 90 Issue 1/2, p91-108. 18p. - Publication Year :
- 2024
-
Abstract
- This paper deals with a weaker form of the property so called L o , o for operators, which we call the property weak L o , o for operators. We characterize this property in terms of convergence of approximate norm attainment sets and prove that a pair of Banach spaces (X, Y) satisfies the property weak L o , o for compact operators if and only if X is reflexive. We further investigate the property weak L o , o for bilinear maps and obtain a connection of it with the property weak L o , o for operators. Importantly, we also characterize some geometric properties of Banach spaces with the help of convergence of approximate norm attainment sets. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BANACH spaces
*GEOMETRY
*TENSOR products
Subjects
Details
- Language :
- English
- ISSN :
- 00016969
- Volume :
- 90
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Acta Scientiarum Mathematicarum
- Publication Type :
- Academic Journal
- Accession number :
- 177003196
- Full Text :
- https://doi.org/10.1007/s44146-023-00095-6