NUMERICAL RANGES OF SOME FOGUEL OPERATORS

Muyan Jiang; Ilya M. Spitkovsky

doi:10.7153/oam-2023-17-14

NUMERICAL RANGES OF SOME FOGUEL OPERATORS

Muyan Jiang, Ilya M. Spitkovsky

Mathematics

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

Abstract

The Foguel operator is defined as (Formula presented), where S is the right shift on a Hilbert space H and T is an arbitrary bounded linear operator acting on H. Obviously, the numerical range W(F₀) of F_T with T = 0 is the open unit disk, and it was suggested by Gau, Wang and Wu in their Linear Algebra and Applications (2021) paper that W(F_aI) for non-zero (Formula presented) might be an elliptical disk. In this paper, we described W (F_aI) explicitly and, as it happens, it is not.

Original language	English (US)
Article number	OaM-17-14
Pages (from-to)	179-185
Number of pages	7
Journal	Operators and Matrices
Volume	17
Issue number	1
DOIs	https://doi.org/10.7153/oam-2023-17-14
State	Published - Mar 2023

Keywords

Foguel operator
Schur complement
Toeplitz operator
and phrases: Numerical range

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.7153/oam-2023-17-14

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abstract = "The Foguel operator is defined as (Formula presented), where S is the right shift on a Hilbert space H and T is an arbitrary bounded linear operator acting on H. Obviously, the numerical range W(F0) of FT with T = 0 is the open unit disk, and it was suggested by Gau, Wang and Wu in their Linear Algebra and Applications (2021) paper that W(FaI) for non-zero (Formula presented) might be an elliptical disk. In this paper, we described W (FaI) explicitly and, as it happens, it is not.",

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N2 - The Foguel operator is defined as (Formula presented), where S is the right shift on a Hilbert space H and T is an arbitrary bounded linear operator acting on H. Obviously, the numerical range W(F0) of FT with T = 0 is the open unit disk, and it was suggested by Gau, Wang and Wu in their Linear Algebra and Applications (2021) paper that W(FaI) for non-zero (Formula presented) might be an elliptical disk. In this paper, we described W (FaI) explicitly and, as it happens, it is not.

AB - The Foguel operator is defined as (Formula presented), where S is the right shift on a Hilbert space H and T is an arbitrary bounded linear operator acting on H. Obviously, the numerical range W(F0) of FT with T = 0 is the open unit disk, and it was suggested by Gau, Wang and Wu in their Linear Algebra and Applications (2021) paper that W(FaI) for non-zero (Formula presented) might be an elliptical disk. In this paper, we described W (FaI) explicitly and, as it happens, it is not.

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KW - Toeplitz operator

KW - and phrases: Numerical range

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ER -

NUMERICAL RANGES OF SOME FOGUEL OPERATORS

Abstract

Keywords

ASJC Scopus subject areas

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