Automatic continuity for weakly decomposable operators

Ridgley Lange, Sheng-Wang Wang and Yong Zhong

Vol. 171 (1995), No. 1, 245–259

DOI: 10.2140/pjm.1995.171.245

Abstract

The authors introduce a new class of operators that are weakly decomposable relative to the identity, and some of their properties are derived; for example, these operators have the single valued extension property. The main result is that every generalized intertwining of an operator having property (δ) with such a weakly decomposable one is necessarily bounded whenever certain side conditions are satisfied. Examples also show that this class of weakly decomposable operators is not comparable by inclusion to the classical cases (e.g. decomposable operators).

Mathematical Subject Classification 2000

Primary: 47B40

Secondary: 47A11, 47B47

Milestones

Received: 16 June 1990

Revised: 16 November 1994

Published: 1 November 1995