Some applications of Banach algebra techniques


KARAEV M., GÜRDAL M. , SALTAN S.

MATHEMATISCHE NACHRICHTEN, vol.284, no.13, pp.1678-1689, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 284 Issue: 13
  • Publication Date: 2011
  • Doi Number: 10.1002/mana.200910129
  • Title of Journal : MATHEMATISCHE NACHRICHTEN
  • Page Numbers: pp.1678-1689
  • Keywords: Banach algebra, generator, Duhamel product, convolution, integration operator, extended eigenvector, EXTENDED EIGENVALUES, DUHAMEL PRODUCT, SOBOLEV SPACES, WIENER ALGEBRA, OPERATORS, EIGENVECTORS, SUBSPACES

Abstract

We consider some functional Banach algebras with multiplications as the usual convolution product * and the so-called Duhamel product circle star. We study the structure of generators of the Banach algebras (C-(n) [0, 1], *) and (C-(n) [0, 1], circle star). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space L-p [0, 1] by the formula (C-phi f) (x) = f (phi (x)). (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim