An operator T on a Banach space X is called an (m, p)-isometry if it satisfies the equality∑
k= 0mmk (-1) mk‖ Tkx‖ p= 0, for all x∈ X. In this paper we prove that if T is an (n, p) …

We prove that if an isometry A and a nilpotent operator Q of order n commute, then A+ Q is a
strict (2n− 1)-isometry. As an application of the main result, we prove that A+ Q cannot be N …

Perturbation of m‐Isometries by Nilpotent Operators - Bermúdez - 2014 - Abstract and Applied
Analysis - Wiley Online Library Skip to Article Content Skip to Article Information Wiley Online …

The purpose of the present paper is to pursue further study of a class of linear bounded
operators, known as n-quasi-m-isometric operators acting on an infinite complex separable …

For a bounded operator T on a Banach space X, we define β (m, p)(T, x):=∑ k= 0 m (− 1) m−
k (mk)‖ T kx‖ p for all x∈ X. We prove β (m, p)(T, x)≤ 0 for all x∈ X implies β (m− 1, p)(T …

POWERS OF m-ISOMETRIES 1. Introduction The m-isometric operators on a Hilbert space H
have been introduced in the paper [1]. Giv Page 1 POWERS OF m-ISOMETRIES TERESA …

A bounded linear operator T on a Banach space X is called an (m, p)-isometry if it satisfies
the equation k= 0^ m (-1)^ km\choose k ‖ T^ kx ‖^ p= 0, for all x ∈ X. In this paper we …

In this paper we characterize weighted shifts (both unilateral and bilateral) on lp spaces that
are (m, q)-isometries. We explicitly construct the weights of those operators. Properties of …

A Banach space operator T∈ B (X) is A (m, p)-isometric for some A∈ B (X), integer m≥ 1
and p∈(0,∞) if∑ mi= 0 (− 1) m− i (mi)|| ATix|| p= 0 for all x∈ X. If S∈ B (X) is A1 (m, p) …

We generalize the notion of m-isometric operator tuples on Hilbert spaces in a natural way to
operator tuples on normed spaces. This is done by defining a tuple analogue of (m, p) …