Generalized resolvents of symmetric and isometric operators: the Shtraus approach

TL;DR

This paper provides a comprehensive exposition of Shtraus's theory on generalized resolvents of symmetric and isometric operators, including full proofs and corrections, offering an alternative to Krein-type formulas.

Contribution

It presents a detailed, corrected exposition of Shtraus's theory with full proofs, enhancing understanding of generalized resolvents in operator theory.

Findings

Provides explicit formulas for generalized resolvents

Clarifies and corrects existing proofs in the theory

Offers a comprehensive exposition with full proofs

Abstract

This exposition paper is devoted to the theory of Abram Vilgelmovich Shtraus and his disciples and followers. This theory studies the so-called generalized resolvents of symmetric and isometric operators in a Hilbert space and provides alternative formulas to the well-known Krein-type formulas. We think that it would be convenient to have an exposition of the corresponding theory with full proofs and necessary corrections.