Some applications of Banach algebra techniques

KARAEV M., GÜRDAL M., SALTAN S.

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

  • Publication Type: Article / Article
  • Volume: 284 Issue: 13
  • Publication Date: 2011
  • Doi Number: 10.1002/mana.200910129
  • Journal Name: MATHEMATISCHE NACHRICHTEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • 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
  • Süleyman Demirel University Affiliated: Yes

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