Paranormal operators and some operator equations

Il Ju An; Eungil Ko

doi:10.2298/FIL1506195A

Paranormal operators and some operator equations

Il Ju An, Eungil Ko

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let a pair (A; B) of bounded linear operators acting on a Hilbert space be a solution of the operator equations ABA = A² and BAB = B². When A is a paranormal operator, we explore some behaviors of the operators AB, BA, and B. In particular, if A or A^* is a polynomial root of paranormal operators, we show that Weyl type theorems are satisfied for the operators AB, BA, and B.

Original language	English
Pages (from-to)	1195-1207
Number of pages	13
Journal	Filomat
Volume	29
Issue number	6
DOIs	https://doi.org/10.2298/FIL1506195A
State	Published - 2015

Keywords

Generalized Weyl’s theorem
Paranormal operator
Single valued extension property

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10.2298/FIL1506195A

Cite this

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AB - Let a pair (A; B) of bounded linear operators acting on a Hilbert space be a solution of the operator equations ABA = A2 and BAB = B2. When A is a paranormal operator, we explore some behaviors of the operators AB, BA, and B. In particular, if A or A* is a polynomial root of paranormal operators, we show that Weyl type theorems are satisfied for the operators AB, BA, and B.

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KW - Single valued extension property

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Paranormal operators and some operator equations

Abstract

Keywords

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