On the kernel and cokernel of some toeplitz operators

Torsten Ehrhardt, Ilya Spitkovsky

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We show that the kernel and/or cokernel of a block Toeplitz operator T (G) are trivial if its matrix-valued symbol G satisfies the condition G(t−1)G(t)*=ING(t−1)G(t)*=IN. As a consequence, the Wiener–Hopf factorization of G (provided it exists) must be canonical. Our setting is that of weighted Hardy spaces on the unit circle. We extend our result to Toeplitz operators on weighted Hardy spaces on the real line, and also Toeplitz operators on weighted sequence spaces.

Original languageEnglish (US)
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Pages127-144
Number of pages18
DOIs
StatePublished - Jan 1 2013

Publication series

NameOperator Theory: Advances and Applications
Volume237
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Fingerprint

Toeplitz Operator
Weighted Hardy Space
kernel
Wiener-Hopf Factorization
Sequence Space
Weighted Spaces
Unit circle
Real Line
Trivial

Keywords

  • Discrete convolution operators
  • Partial indices
  • Toeplitz operators
  • Wiener–Hopf factorization

ASJC Scopus subject areas

  • Analysis

Cite this

Ehrhardt, T., & Spitkovsky, I. (2013). On the kernel and cokernel of some toeplitz operators. In Operator Theory: Advances and Applications (pp. 127-144). (Operator Theory: Advances and Applications; Vol. 237). Springer International Publishing. https://doi.org/10.1007/978-3-0348-0639-8_10

On the kernel and cokernel of some toeplitz operators. / Ehrhardt, Torsten; Spitkovsky, Ilya.

Operator Theory: Advances and Applications. Springer International Publishing, 2013. p. 127-144 (Operator Theory: Advances and Applications; Vol. 237).

Research output: Chapter in Book/Report/Conference proceedingChapter

Ehrhardt, T & Spitkovsky, I 2013, On the kernel and cokernel of some toeplitz operators. in Operator Theory: Advances and Applications. Operator Theory: Advances and Applications, vol. 237, Springer International Publishing, pp. 127-144. https://doi.org/10.1007/978-3-0348-0639-8_10
Ehrhardt T, Spitkovsky I. On the kernel and cokernel of some toeplitz operators. In Operator Theory: Advances and Applications. Springer International Publishing. 2013. p. 127-144. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-0348-0639-8_10
Ehrhardt, Torsten ; Spitkovsky, Ilya. / On the kernel and cokernel of some toeplitz operators. Operator Theory: Advances and Applications. Springer International Publishing, 2013. pp. 127-144 (Operator Theory: Advances and Applications).
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