An operator T on a Banach space X is called anIn this paper we prove that if T is an (n, p)-isometry, S is an (m, p)-isometry and they commute, then TS is an (m + n − 1, p)-isometry.This result applied to elementary operators of length 1 defined on the Hilbert-Schmidt class proves a conjecture in [11].

No abstract

We prove that ifTis anm-isometry on a Hilbert space andQann-nilpotent operator commuting withT, thenT+Qis a2n+m-2-isometry. Moreover, we show that a similar result form, q-isometries on Banach spaces is not true.

No abstract

No abstract