Acta mathematica scientia, Series B >

2017 , Vol. 37 >Issue 6: 1695 - 1704

DOI: https://doi.org/10.1016/S0252-9602(17)30101-7

Articles

HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES

  • Jongrak LEE
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  • Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, Republic of Korea

Received date: 2016-07-18

  Revised date: 2017-04-19

  Online published: 2017-12-25

Supported by

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).

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Abstract

In this paper we consider the block Toeplitz operators TΦ on the weighted Bergman space Aα2(D, Cn) and we give a necessary and sufficient condition for the hyponormality of block Toeplitz operators with symbol in the class of functions Φ=F + G* with matrix-valued polynomial functions F and G with degree 2.

Key words： block Toeplitz operators; hyponormal; weighted Bergman space

Cite this article

Jongrak LEE . HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES[J]. Acta mathematica scientia, Series B, 2017 , 37(6) : 1695 -1704 . DOI: 10.1016/S0252-9602(17)30101-7

References

[1] Axler S. Bergman Spaces and Their Operators//Surveys of Some Recent Results in Operator Theory, Vol I. Pitman Research Notes in Mathematics, 1988, 171:1-50[2] Cowen C. Hyponormality of Toeplitz operators. Proc Amer Math Soc, 1988, 103:809-812[3] Curto R E, Hwang I S, Lee W Y. Hyponormality and subnormality of block Toeplitz operators. Adv Math, 2012, 230:2094-2151[4] Gu C, Hendricks J, Rutherford D. Hyponormality of block Toeplitz operators. Pacific J Math, 2006, 223:95-111[5] Hedenmalm H, Korenblum B, Zhu K. Theory of Bergman Spaces. New York:Springer-Verlag, 2000[6] Hwang I S, Kang D O, Lee W Y. A gap between hyponormality and subnormality for block Toeplitz operators. J Math Anal Appl, 2011, 382:883-891[7] Hwang I S, Lee J. Hyponormal Toeplitz operators on the weighted Bergman spaces. Math Inequal Appl, 2012, 15:323-330[8] Hwang I S, Lee J, Park S W. Hyponormal Toeplitz operators with polynomial symbols on weighted Bergman spaces. J Inequal Appl, 2014:1-8
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