Abstract

If $T$ and $S$ are Hilbert space operators obeying generalized a-Weyl's theorem, then it does not necessarily imply that the direct sum $T\oplus S$ obeys generalized a-Weyl's theorem. In this paper we explore certain conditions on $T$ and $S$ so that the direct sum $T\oplus S$ obeys generalized a-Weyl's theorem.

Keywords: Direct sums, generalized Weyl's theorem, generalized a-Weyl's theorem, generalized a-Browder's theorem.

MSC: 47A10, 47A11, 47A53

Pages:  265$-$270     

Volume  62 ,  Issue  4 ,  2010