Composition operators whose symbols have orthogonal powers

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Composition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non-inner map with a fixed point in the unit disk. The canonical decomposition of a non-unitary composition contraction is determined.

Original languageEnglish (US)
Pages (from-to)845-857
Number of pages13
JournalHouston Journal of Mathematics
Volume37
Issue number3
StatePublished - Dec 26 2011

Fingerprint

Composition Operator
Unit Disk
Canonical Decomposition
Essential Spectrum
Spectral Radius
Hardy Space
Hilbert
Contraction
Fixed point
If and only if
Arbitrary
Operator

Keywords

  • Composition operator
  • Rudin's orthogonality condition

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Composition operators whose symbols have orthogonal powers. / Matache, Valentin.

In: Houston Journal of Mathematics, Vol. 37, No. 3, 26.12.2011, p. 845-857.

Research output: Contribution to journalArticle

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