Weyl's theorem for algebrascally wF(p,r,q) operators with p,q>0 and q≥1

• Main Author: Rashid, M.H.M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Series: Український математичний журнал
• Subjects: Статті
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/166357

If T or T∗ is an algebraically wF(p,r,q) operator with p,r>0 and q≥1 acting on an infinite-dimensional separable Hilbert space, then we prove that the Weyl theorem holds for f(T), for every f∈Hol(σ(T)), where Hol(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T∗ is a wF(p,r,q) operator with p,r>0 and q≥1, then the a-Weyl theorem holds for f(T). Also, if T or T∗ is an algebraically wF(p,r,q) operators with p,r>0 and q≥1, then we establish spectral mapping theorems for the Weyl spectrum and essential approximate point spectrum of T for every f∈Hol(σ(T)), respectively. Finally, we examine the stability of the Weyl theorem and a-Weyl theorem under commutative perturbation by finite-rank operators.