Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 1 (2019), 174-191.
On some geometric properties of operator spaces
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 and , assuming to be reflexive. We also characterize parallelism of two bounded linear operators between normed linear spaces and . 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 is a semirotund space which is not strictly convex if are finite-dimensional Banach spaces and is strictly convex.
Banach J. Math. Anal., Volume 13, Number 1 (2019), 174-191.
Received: 15 February 2018
Accepted: 22 June 2018
First available in Project Euclid: 4 December 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]
Mal, Arpita; Sain, Debmalya; Paul, Kallol. On some geometric properties of operator spaces. Banach J. Math. Anal. 13 (2019), no. 1, 174--191. doi:10.1215/17358787-2018-0021. https://projecteuclid.org/euclid.bjma/1543914019