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

  • M. H. M. Rashid Mu’tah Univ., Al-Karak, Jordan


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 $f \in \text{Hol}(\sigma(T))$, where $ \text{Hol}(\sigma(T))$ denotes the set of all analytic functions in an open neighborhood of $\sigma(T)$. 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 $f \in \text{Hol}(\sigma(T))$, respectively. Finally, we examine the stability of the Weyl theorem and $a$-Weyl theorem under commutative perturbation by finite-rank operators.
How to Cite
Rashid, M. H. M. “Weyl’s Theorem for Algebrascally $wF(p, R, q)$ Operators With $p, Q > 0$ and $q \geq 1$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 8, Aug. 2011, pp. 1092-0, https://umj.imath.kiev.ua/index.php/umj/article/view/2787.
Research articles