Toeplitz Operators with Non-trivial Kernels and Non-dense Ranges on Weak Hardy Spaces

Oleksiy Karlovych*, Eugene Shargorodsky

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Citation (Scopus)

Abstract

The well known Coburn lemma can be stated as follows: a nonzero Toeplitz operator T(a) with symbol a∈ L has a trivial kernel or a dense range on the Hardy space Hp with p ∈ (1, ∞). We show that an analogue of this result does not hold for the Hardy-Marcinkiewicz (weak Hardy) spaces Hp, with p ∈ (1, ∞): there exist continuous nonzero functions a: Depending on p such that dim (Ker T(a) ) = ∞ and (Forumala Presented).

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Pages463-476
Number of pages14
DOIs
Publication statusPublished - 2022

Publication series

NameOperator Theory: Advances and Applications
Volume289
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Blaschke product
  • Coburn’s lemma
  • Hardy-Marcinkiewicz space
  • Kernel
  • Range
  • Toeplitz operator

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