Bull. Korean Math. Soc. 1998 Vol. 35, No. 1, 91-97
Youngoh Yang Cheju National University
Abstract : In this paper we study the Weyl spectrum of weight $\alpha$, $\omega_\alpha(T)$, of an operator $T$ acting on an infinite dimensional Hilbert space. Main results are as follows. Firstly, we show that the Weyl spectrum of weight $\alpha$ of a polynomially $\alpha$-compact operator is finite, and that similarity preserves polynomial $\alpha$-compactness and the $\alpha$-Weyl's theorem both. Secondly, we give a sufficient condition for an operator to be the sum of an unitary and a $\alpha$-compact operators.