Journal of the
Korean Mathematical Society JKMS

For a bounded linear operator $T$ on a separable complex infinite dimensional Hilbert space $\mathcal{H}$, we say that $T$ is a quasi-class $(A,k)$ operator if ${T^*}^k|T^2|T^k\ge {T^*}^k|T|^2T^k$. In this paper we prove that if $T$ is a quasi-class $(A,k)$ operator and $f$ is an analytic function on an open neighborhood of the spectrum of $T$, then $f(T)$ satisfies Weyl's theorem. Also, we consider the tensor product for quasi-class $(A,k)$ operators.

Keywords: quasi-class $(A,k)$ operator, Weyl's theorem, tensor product

MSC numbers: 47A53, 47B20