On the generalized resolvents of isometric operators with gaps

TL;DR

This paper extends and corrects previous results on the generalized resolvents of isometric operators with spectral gaps, providing new proofs and generalizations of existing theorems.

Contribution

It offers corrections, generalizations, and new proofs related to the generalized resolvents of isometric operators with gaps in their spectrum.

Findings

Corrected and generalized previous results on resolvents

Provided analogs of McKelvey's results

Included a short proof of Inin's formula

Abstract

In this paper we obtain some slight correction and generalization of the results of Ryabtseva on the generalized resolvents for isometric operators with a gap in their spectrum. Also, analogs of some McKelvey's results and a short proof of Inin's formula for the generalized resolvents of an isometric operator are obtained.