Weak sequential properties of the multiplication operators on Banach algebras

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OKTAY O.

Quaestiones Mathematicae, cilt.45, sa.9, ss.1333-1342, 2022 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 9
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2989/16073606.2021.1943038
  • Dergi Adı: Quaestiones Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1333-1342
  • Anahtar Kelimeler: Joint weak sequential continuity
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Uşak Üniversitesi Adresli: Evet

Özet

Let A be a Banach algebra. For f ∈ A*, we inspect the weak sequential properties of the well-known map Tf : A → A*, Tf (a) = fa, where fa ∈ A* is defined by fa(x) = f (ax) for all x ∈ A. We provide equivalent conditions for when Tf is completely continuous for every f ∈ A*, and for when Tf maps weakly precompact sets onto L-sets for every f ∈ A*. Our results have applications to the algebra of compact operators K(X) on a Banach space X.