On Simultaneous Triangularization of Matrices and Quasinilpotency of Commutator of Compact Operators

2024/01/30 by Sasmita Patnaik, Patnaik, Sasmita, Rahul Sethi +1
Computer Science · Mathematics · #15A15 #47A08 #47A10 #47B02 #47B47 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2401.16916

openalex publication_date 2024/01/30 · openalex created_date 2024/02/01 · openalex updated_date 2026/07/28

Abstract

In this paper we determine a sufficient condition for the quasinilpotency of a commutator of compact operators via block-tridiagonal matrix form associated with a compact operator. We also prove that every compact operator is unitarily equivalent to the sum of a compact quasinilpotent operator and a triangularizable compact operator.

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