2020/06/11 by Anubhab Ray, Debmalya Sain, Ray, Anubhab +5
Mathematics · #Advanced Banach Space Theory #Holomorphic and Operator Theory #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2006.06440
We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if T, A ∈ \mathbbL(\mathbbX, \mathbbY) satisfy T \botB A, then whether there exists x ∈ \mathbbX such that Tx\botB Ax with ‖x‖ =1, ‖Tx‖ = ‖T‖, where \mathbbX, \mathbbY are normed linear spaces. In this context, we introduce the notion of Property Pn for a Banach space and illustrate its connection with orthogonality of a bounded linear operator between Banach spaces. We further study Property Pn for various polyhedral Banach spaces.