Simpler Proof of the Ringrose's Characterization of Compact Operators

Authors

  • Aydin Shukurov Institute of Mathematics and Mechanics NAS of Azerbaijan; Baku State University

Keywords:

orthonormal sequence and orthonormal bases in Hilbert space, Ringrose's characterization of compact operators, linear operators, compact operators

Abstract

The aim of this note is to give short, simpler and elementary proof of one characterization of compact operators via orthonormal sequences, which, hopefully will make this fact more accessible to nonspecialists and to a wide audience (especially to students). Beside this, the proof given here shows that this fact holds true for operator acting from Hilbert space to some Banach (not necessarily Hilbert) space.

Author Biography

  • Aydin Shukurov, Institute of Mathematics and Mechanics NAS of Azerbaijan; Baku State University
    Functional Analysis; Research Fellow

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Published

2015-10-28

Issue

Vol. 8 No. 4: (October 2015)

Section

Functional Analysis

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How to Cite

Simpler Proof of the Ringrose’s Characterization of Compact Operators. (2015). European Journal of Pure and Applied Mathematics, 8(4), 499-501. https://www.ejpam.com/index.php/ejpam/article/view/2371