Some Convergence Theorems for Operator Sequences

Mustafayev H.

INTEGRAL EQUATIONS AND OPERATOR THEORY, cilt.92, sa.4, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 92 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00020-020-02591-8
  • Dergi Adı: INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Hilbert space, Banach space, Compact operator, Toeplitz operator, Composition operator, Model operator, Local spectrum, Operator sequence, Operator average, Convergence
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Let A, T, and B be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences {A(n)TB(n)} and {1/n Sigma(n-1)(i=0) A(i)TB(i)}. These results are applied to the Toeplitz, composition, and model operators. Some related problems are also discussed.