Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces | Zendy

Mübariz Garayev | Zendy; Mehmet Gürdal | Zendy

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Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces

Author(s) -

Mübariz Garayev,

Mehmet Gürdal

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1706-93

Subject(s) - toeplitz matrix , mathematics , zero (linguistics) , hardy space , product (mathematics) , space (punctuation) , combinatorics , product topology , pure mathematics , mathematical analysis , geometry , linguistics , philosophy

In this article, we are interested in the zero Toeplitz product problem: for two symbols f, g ∈ L∞ (D, dA) , if the product TfTg is identically zero on L 2 a (D) , then can we claim Tf or Tg is identically zero? We give a particular solution of this problem. A new proof of one particular case of the zero Toeplitz product problem in the Hardy space H (D) is also given.

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