$(S+N)$-triangular operators: spectral properties and important examples

TL;DR

This paper introduces $(S+N)$-triangular operators in Hilbert spaces, generalizing spectral operators, and demonstrates that many classes of operators are encompassed by this new concept.

Contribution

The paper defines $(S+N)$-triangular operators, extending spectral operator theory, and shows that many operators fit into this new framework.

Findings

Many classes of operators are $(S+N)$-triangular.

Properties of $(S+N)$-triangular operators align with spectral operators.

The notion broadens the scope of spectral operator theory.

Abstract

We introduce a notion of $(S+N)$-triangular operators in the Hilbert space using some basic ideas from triangular representation theory. Our notion generalizes the well-known notion of the spectral operators so that many properties of the $(S+N)$-triangular operators coincide with those of spectral operators. At the same time we show that wide classes of operators are $(S+N)$-triangular.