Property (ω) and quasi-class (A, k) operators

• M. H. M. Rashid ^[1]
  1. [1] Mu’tah University
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 52, Nº. 1, 2011, págs. 133-142
• Idioma: inglés
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• Resumen

  • In this paper, we prove the following assertions: (i) If T is of quasi-class (A, k), then T is polaroid and reguloid; (ii) If T or T* is an algebraically of quasi-class (A, k) operator, then Weyls theorem holds for f(T) for every f ∈ Hol(σ(T)); (iii) If T* is an algebraically of quasi-class (A, k) operator, then a-Weyls theorem holds for f(T) for every f ∈ Hol(σ(T)); (iv) If T* is algebraically of quasi-class (A, k) then property (ω) holds for T.