Biorthogonal vectors, sesquilinear forms and some physical operators

TL;DR

This paper explores properties of non-self-adjoint operators and sesquilinear forms derived from biorthogonal vector families, focusing on their behavior when forming $ ext{D}$-quasi bases, extending previous analyses.

Contribution

It advances understanding of non-self-adjoint operators and sesquilinear forms associated with biorthogonal systems, especially in the context of $ ext{D}$-quasi bases.

Findings

Analysis of non-self-adjoint operators in biorthogonal systems

Properties of sesquilinear forms from generalized Riesz systems

Behavior of these forms when forming $ ext{D}$-quasi bases

Abstract

Continuing the analysis undertaken in previous articles, we discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the so-called generalized Riesz systems, enjoying certain properties. In particular we discuss what happens when they forms two $\D$-quasi bases.