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

Garayev M. T., GÜRDAL M.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.3, pp.1504-1508, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1706-93
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1504-1508
  • Keywords: Toeplitz operator, Bergman space, Hardy space, zero Toeplitz product, Berezin symbol, BEREZIN, OPERATORS
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this article, we are interested in the zero Toeplitz product problem: for two symbols f, g is an element of L-infinity (D, dA), if the product TfTg is identically zero on L-a(2)(D), then can we claim T-f or T-g 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-2 (D) is also given.