Difference Inequalities for the Groups and Semigroups of Operators on Banach Spaces

Mustafayev H.

COMPLEX ANALYSIS AND OPERATOR THEORY, vol.6, no.6, pp.1241-1267, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 6
  • Publication Date: 2012
  • Doi Number: 10.1007/s11785-010-0126-x
  • Journal Name: COMPLEX ANALYSIS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1241-1267
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Let T = {T (t)}(t is an element of R) be a sigma(X, F)-continuous group of isometries on a Banach space X with generator A, where sigma(X, F) is an appropriate local convex topology on X induced by functionals from F subset of X*. Let sigma(A)(x) be the local spectrum of A at x is an element of X and r(A)(x) := sup{|lambda| : lambda is an element of sigma(A)(x)}, the local spectral radius of A at x. It is shown that for every x is an element of X and tau is an element of R,