On hyponormality on the Bergman space of an annulus On hyponormality on the Bergman space of an annulus

A bounded operator S on a Hilbert space is hyponormal if S ∗ S - S S ∗ is positive. In this work we find necessary conditions for the hyponormality of the Toeplitz operator T φ + ψ ¯ on the Bergman space of the annulus 1 / 2 < | z | < 1 where both φ and ψ are bounded and analytic on the annulu...

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Bibliographic Details
Published inIndian journal of pure and applied mathematics Vol. 56; no. 2; pp. 848 - 858
Main Authors Sadraoui, Houcine, Halouani, Borhen
Format Journal Article
LanguageEnglish
Published New Delhi Indian National Science Academy 01.06.2025
Springer Nature B.V
Subjects
Annuli
Applications of Mathematics
Hilbert space
Mathematics
Mathematics and Statistics
Numerical Analysis
Operators (mathematics)
Original Research
Positive matrices
Secondary 15B48
15B05
Hyponormal
Primary 47B35
47B20
Toeplitz operators
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ISSN0019-5588
0975-7465
DOI10.1007/s13226-023-00525-9

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Summary:A bounded operator S on a Hilbert space is hyponormal if S ∗ S - S S ∗ is positive. In this work we find necessary conditions for the hyponormality of the Toeplitz operator T φ + ψ ¯ on the Bergman space of the annulus 1 / 2 < | z | < 1 where both φ and ψ are bounded and analytic on the annulus and are of the form ∑ n ≥ 1 a n z n + b n 1 z n .
Bibliography:ObjectType-Article-1
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ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-023-00525-9