COMPACT OPERATORS IN THE COMMUTANT OF ESSENTIALLY NORMAL OPERATORS


Mustafayev H., HUSEYNOV F. B.

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol.8, no.2, pp.1-15, 2014 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.15352/bjma/1396640047
  • Journal Name: BANACH JOURNAL OF MATHEMATICAL ANALYSIS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1-15

Abstract

Let T be a bounded, linear operator on a complex, separable, infinite dimensional Hilbert space H. We assume that T is an essentially isometric (resp. normal) operator, that is, I-H - T*T (resp. TT* - T*T) is compact. For the compactness of S from the commutant of T, some necessary and sufficient conditions are found on S. Some related problems are also discussed.