WEYL'S TYPE THEOREMS FOR ALGEBRAICALLY (p, k)-QU ASIHYPONORMAL OPERATORS

For a bounded linear operator T we prove the following as-sertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is alpha-isoloid, polaroid, reguloid and alpha-polaroid. (b) If T* is algebraically (p, k)quasihyponormal, then alpha-Weyl's theorem holds for f(T) for every f epsilon Hol(sigma(T)), where Hol(sigma(T)) is the space of all functions that analytic in an open neighborhoods of sigma(T) of T. (c) If T* is algebraically (p, k)-quasihyponormal, then generalized sigma-Weyl's theorem holds for f(T) for every f epsilon Hol(sigma(T)). (d) If T is a (p,k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum sigma(-)(sBF+)(T), and for left Drazin spectrum sigma(lD)(T) for every f epsilon Hol(sigma(T)).