Local Spectra of Unilateral Operator Weighted Shifts

Abstract

In this note, the local spectral properties of unilateral operator weighted shifts are studied.

Spectrum of bilateral shifts with operator-valued weights

“…We shall proceed as in [4] in order to prove this result. It follows from Lemma 2.2 that each S e i satisfies Dunford's condition (C) (see also [1, Theorem 2.79]).…”

“…In [4], the author described the local spectrum of S at most points of l 2 (Z, H) and used some tools from local spectral theory to describe completely the spectrum of all bilateral operator-weighted shifts satisfying Dunford's condition (C) (see [4,Theorem 4.2]). …”