On numerical radius and Crawford number attainment sets of a bounded linear operator

2020/01/27 by ‎Debmalya Sain, ‎Arpita Mal, Sain, Debmalya +5
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Primary 47A12 #Secondary 46B20

paper · pdf · doi:10.48550/arxiv.2001.09720

openalex publication_date 2020/01/27 · openalex created_date 2020/01/30 · openalex updated_date 2026/07/28

Abstract

We completely characterize the Crawford number attainment set and the numerical radius attainment set of a bounded linear operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical radius, Crawford number, norm, minimum norm of a bounded linear operator defined on a normed space. Our study illustrates the similarities and the differences of the extremal properties of a bounded linear operator on a Hilbert space and a general normed space.

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