In this paper, we introduce the class of n-quasi-(m, C)-isometric operator on a Hilbert space
which is a variation of (m, C)-isometric operators Cho M, Ko E, Lee JE.[On (m, C)-isometric …

Structure of elementary operators defining m-left invertible, m-selfadjoint and related classes
of operators - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books …

A Banach space operator T∈ B (X) has a left m-inverse (resp., an essential left m-inverse)
for some integer m≥ 1 if there exists an operator S∈ B (X)(resp., an operator S∈ B (X) and …

Given Hilbert space operators T, S∈ B (ℋ), let Δ and δ∈ B (B (ℋ)) denote the elementary
operators Δ T, S (X)=(LTRS− I)(X)= TXS− X and δ T, S (X)=(LT− RS)(X)= TX− XS. Let d= Δ or …

We study left n-invertible operators introduced in two recent papers. We show how to
construct a left n-inverse as a sum of a left inverse and a nilpotent operator. We provide …

Generalising the definition to commuting d-tuples of operators, a number of authors have
considered structural properties of m-isometric, n-symmetric and (m, n)-isosymmetric …

The study of tuples of commuting operators was the subject of intensive study by many
authors. Our aim in this work is to consider a generalization of the notions of m-partial …

Class of operators related to a $(m,C)$ -isometric tuple of commuting operators | SpringerLink
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We prove some further properties of the operator T∈[nQN](n‐power quasinormal, defined in
Sid Ahmed, 2011). In particular we show that the operator T∈[nQN] satisfying the translation …

A Hilbert space operator A∈ B (H) is left (X, m)-invertible by B∈ B (H)(resp., B∈ B (H) is an
(X, m)-adjoint of A∈ B (H)) for some operator X∈ B (H) if△ B, A m (X)=∑ j= 0 m (− 1) j (mj) B …