On a joint $(m, (q_1, ..., q_d))$-partial isometries and a joint $m$-invertible $d$-tuple of operators on a Hilbert space

TL;DR

This paper introduces and studies the concepts of (m, (q_1, ..., q_d))-partial isometries and m-invertibility for tuples of operators on a Hilbert space, generalizing existing notions in operator theory.

Contribution

It defines new classes of operators and extends the concept of m-invertibility to operator tuples, broadening the theoretical framework.

Findings

Defined (m, (q_1, ..., q_d))-partial isometries.

Introduced the notion of m-invertibility for operator tuples.

Provided foundational properties and potential applications.

Abstract

The aim of the present paper is, firstly we study the concepts of (m, (q_1, ..., q_d))- partial isometries on a Hilbert space, secondly, we introduce the notion of m- invertibility of tuples of operators as a natural generalization of the m-invertibility in single variable operators.