In the paper, we prove the following assertions: (1) If $T$ is an algebraically quasi-$*$-$A$ operator, then $T$ is polaroid. (2) If $T$ or $T^{*}$ is an algebraically quasi-$*$-$A$ operator, then Weyl's theorem holds for $f(T)$ for every $f \in H(\sigma(T))$. (3) If $T^{*}$ is an algebraically quasi-$*$-$A$ operator, then a-Weyl's theorem holds for $f(T)$ for every $f \in H(\sigma(T))$.
Banach J. Math. Anal.
7(1):
107-115
(2013).
DOI: 10.15352/bjma/1358864552
