Hyponormality of Toeplitz Operators on Symmetric-type Circulant Trigonometric Polynomial Symbols: An Extremal Case

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DOI:

https://doi.org/10.26713/cma.v15i3.2891

Keywords:

Toeplitz operators, Hyponormal operators, Circulant trigonometric polynomials, Symmetric-type trigonometric polynomials

Abstract

In this paper, we give some necessary and sufficient conditions to determine the hyponormality of Toeplitz operators on symmetric-type circulant trigonometric polynomial symbols in Hardy-Hilbert spaces of analytic functions considering an extremal case.

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References

C. C. Cowen, Hyponormality of Toeplitz operators, Proceedings of the American Mathematical Society 103(3) (1988), 809 – 812, DOI: 10.1090/S0002-9939-1988-0947663-4.

Z. Cuckovic, and R.E. Curto, A new necessary condition for the hyponormality of Toeplitz operators on the Bergman space, Journal of Operator Theory 79(2) (2018), 287 – 300, URL: https://www.theta.ro/jot/archive/2018-079-002/2018-079-002-002.html.

D. R. Farenick and W. Y. Lee, Hyponormality and spectra of Toeplitz operators, Transactions of the American Mathematical Society 348(10) (1996), 4153 – 4174, DOI: 10.1090/S0002-9947-96-01683-2.

D. R. Farenick and W. Y. Lee, On hyponormal Toeplitz operators with polynomial and circulant-type symbols, Integral Equations and Operator Theory 29 (1997), 202 – 210, DOI: 10.1007/BF01191430.

M. Fleeman and C. Liaw, Hyponormal Toeplitz operators with non-harmonic Symbol acting on the Bergman space, Operators and Matrices 13(1) (2019), 61 – 83, DOI: 10.7153/oam-2019-13-04.

A. Gupta and A. Aggarwal, Hyponormality of the sum of Toeplitz operators with non-harmonic symbol on the Fock space, Operators and Matrices 18 (2024), 147 – 162, DOI: 10.7153/oam-2024-18-10.

M. Hazarika and A. Phukon, On hyponormality of trigonometric Toeplitz operators, International Journal of Functional Analysis, Operator Theory and Applications 3(2) (2011), 163 – 189, URL: http://www.pphmj.com/abstract/6382.htm.

I. H. Kim and W. Y. Lee, On hyponormal toeplitz operators with polynomial and symmetric-type symbols, Integral Equations and Operator Theory 32 (1998), 216 – 233, DOI: 10.1007/BF01196519.

S. Kim, E. Ko, J. E. Lee and J. Lee, H-Toeplitz operators on the function spaces, Monatshefte für Mathematik 205 (2024), 757 – 786, DOI: 10.1007/s00605-024-01985-9.

T. Le and B. Simanek, Hyponormal Toeplitz operators on weighted Bergman spaces, Integral Transforms and Special Functions 32(5-8) (2021), 560 – 567, DOI: 10.1080/10652469.2020.1751153.

R. A. Martínez-Avendaño and P. Rosenthal, An Introduction to Operators on the Hardy-Hilbert Space, Graduate Texts in Mathematics series, Volume 237, Springer, New York, xii + 220 pages (2007), DOI: 10.1007/978-0-387-48578-2.

T. Nakazi and K. Takahashi, Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Transactions of the American Mathematical Society 338 (1993), 753 – 767, DOI: 10.1090/S0002-9947-1993-1162103-7.

A. Phukon, On hyponormal Toeplitz operators with trigonometric polynomial symbols, Communications in Mathematics and Applications 6(2) (2015), 49 – 54, DOI: 10.26713/cma.v6i2.317.

H. Sadraoui, M. Garayev and H. Guediri, On hyponormality of Toeplitz operators, Rocky Mountain Journal of Mathematics 51(5) (2021), 1821 – 1831, DOI: 10.1216/rmj.2021.51.1821.

B. Simanek, Hyponormal Toeplitz operators with non-harmonic algebraic symbol, Analysis and Mathematical Physics 9 (2019), 1613 – 1626, DOI: 10.1007/s13324-018-00279-2.

K. Zhu, Hyponormal Toeplitz operators with polynomial symbols, Integral Equations and Operator Theory 21 (1995), 376 – 381, DOI: 10.1007/BF01299971.

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Published

30-11-2024
CITATION

How to Cite

Phukon, A., & Narzary, N. (2024). Hyponormality of Toeplitz Operators on Symmetric-type Circulant Trigonometric Polynomial Symbols: An Extremal Case. Communications in Mathematics and Applications, 15(3), 959–968. https://doi.org/10.26713/cma.v15i3.2891

Issue

Vol. 15 No. 3 (2024)

Section

Research Article

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