Open Access
January 2019 On some geometric properties of operator spaces
Arpita Mal, Debmalya Sain, Kallol Paul
Banach J. Math. Anal. 13(1): 174-191 (January 2019). DOI: 10.1215/17358787-2018-0021


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 B ( X , Y ) is a semirotund space which is not strictly convex if X , Y are finite-dimensional Banach spaces and Y is strictly convex.


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Arpita Mal. Debmalya Sain. Kallol Paul. "On some geometric properties of operator spaces." Banach J. Math. Anal. 13 (1) 174 - 191, January 2019.


Received: 15 February 2018; Accepted: 22 June 2018; Published: January 2019
First available in Project Euclid: 4 December 2018

zbMATH: 07002037
MathSciNet: MR3892339
Digital Object Identifier: 10.1215/17358787-2018-0021

Primary: 46B20
Secondary: 47L05

Keywords: norm attainment , norm-parallelism , orthogonality , semirotund

Rights: Copyright © 2019 Tusi Mathematical Research Group

Vol.13 • No. 1 • January 2019
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