Truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators

TL;DR

This paper investigates truncated moment problems for specific classes of operators in indefinite inner product spaces, providing solvability conditions, canonical solutions, and extension results for related operators.

Contribution

It introduces new solvability criteria and constructs canonical solutions for truncated moment problems involving $J$-self-adjoint, $J$-skew-self-adjoint, and $J$-unitary operators.

Findings

Derived solvability conditions for the moment problems.

Constructed explicit canonical solutions.

Obtained extension results for $J$-skew-symmetric and $J$-isometric operators.

Abstract

In this paper we study truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvability are given. Some canonical solutions of the moment problems are constructed. As a by-product, some extension results for $J$-skew-symmetric and $J$-isometric operators are obtained.