Mal, Arpita and Sain, Debmalya and Paul, Kallol (2019) ON SOME GEOMETRIC PROPERTIES OF OPERATOR SPACES. In: BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 13 (1). pp. 174-191.
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Abstract
In this article, we study some geometric properties like parallelism, orthogonality, and semirotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear spaces X and Y, assuming X to be reflexive. We also characterize parallelism of two bounded linear operators between normed linear spaces X and Y. We investigate parallelism and approximate parallelism in the space of bounded linear operators defined on a Hilbert space. Using the characterization of operator parallelism, we study Birkhoff James orthogonality in the space of compact linear operators as well as bounded linear operators. Finally, we introduce the concept of semirotund points (semirotund spaces) which generalizes the notion of exposed points (strictly convex spaces). We further study semirotund operators and prove that M (X, Y) is a semirotund space which is not strictly convex if X, Y are finite-dimensional Banach spaces and Y is strictly convex.
| Item Type: | Journal Article |
|---|---|
| Publication: | BANACH JOURNAL OF MATHEMATICAL ANALYSIS |
| Publisher: | DUKE UNIV PRESS |
| Additional Information: | Copyright of this article belongs to DUKE UNIV PRESS |
| Keywords: | norm-parallelism; orthogonality; semirotund; norm attainment |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 25 Jan 2019 12:52 |
| Last Modified: | 25 Jan 2019 12:52 |
| URI: | http://eprints.iisc.ac.in/id/eprint/61433 |
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