A note on operator tuples which are (m,p)-isometric as well as (μ,∞)-isometric

Abstract

We show that if a tuple of commuting, bounded linear operators (T1, ..., Td) 2 B(X)d is both an (m, p)-isometry and a (μ,1)-isometry, then the tuple (Tm 1 , ..., Tm d ) is a (1, p)-isometry. We further prove some additional properties of the operators T1, ..., Td and show a stronger result in the case of a commuting pair (T1, T2).