Characteristic properties for a generalized resolvent of a pair of commuting isometric operators

TL;DR

This paper introduces a generalized resolvent concept for pairs of commuting isometric operators in Hilbert spaces, establishing their key properties and extending the theoretical framework of operator analysis.

Contribution

It defines and analyzes characteristic properties of a generalized resolvent for commuting isometric operators, advancing the mathematical understanding of such operator pairs.

Findings

Characteristic properties of the generalized resolvent are established.

The paper extends the theoretical framework for commuting isometric operators.

Foundational results for further operator theory research.

Abstract

In this paper we consider a notion of a generalized resolvent for a pair of commuting isometric operators in a Hilbert space $H$. Characteristic properties of the generalized resolvent are obtained.