摘要

In this paper we show that a bounded linear operator on a Banach space X is polaroid if and only if p(T) is polaroid for some polynomial p. Consequently, algebraically paranormal operators defined on Banach spaces are hereditarily polaroid. Weyl type theorems are also established for perturbations f(T + K), where T is algebraically paranormal, K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of T + K, such that f is nonconstant on each of the components of its domain. These results subsume recent results in this area.

  • 出版日期2013