ON THE CONVERGENCE OF ITERATES OF CONVOLUTION OPERATORS IN BANACH SPACES

Mustafayev H.

MATHEMATICA SCANDINAVICA, cilt.126, sa.2, ss.339-366, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 126 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.7146/math.scand.a-119601
  • Dergi Adı: MATHEMATICA SCANDINAVICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.339-366
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Let G be a locally compact abelian group and let M(G) be the measure algebra of G. A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0) parallel to mu(n)parallel to(1) < infinity. Let T = {T-g : g is an element of G} be a bounded and continuous representation of G on a Banach space X. For any mu is an element of M(G), there is a bounded linear operator on X associated with mu, denoted by T-mu, which integrates T-g with respect to mu. In this paper, we study norm and almost everywhere behavior of the sequences {T-mu(n) x} (x is an element of X) in the case when mu, is power bounded. Some related problems are also discussed.