SPECIAL OPERATOR CLASSES AND THEIR PROPERTIES


KARAEV M. T. , Guerdal M., Yamanci U.

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol.7, no.2, pp.74-85, 2013 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.15352/bjma/1363784224
  • Journal Name: BANACH JOURNAL OF MATHEMATICAL ANALYSIS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.74-85
  • Keywords: Compact operator, Schatten-von Neumann classes, Berezin symbol, s-number, Abel convergence., BEREZIN SYMBOLS

Abstract

We introduce some special operator classes and study in terms of Berezin symbols their properties. In particular, we give some characterizations of compact operators and Schatten-von Neumann class operators in terms of Berezin symbols. We also consider some classes of compact operators on a Hilbert space H, which are generalizations of the well known Schatten-von Neumann classes of compact operators. Namely, for any number p, 0 < p < infinity, and the sequence w := (w(n))(n >= 0) of complex numbers w(n), n > 0, we define the following classes of compact operators on H: