On certain spectral features inherent to scalar type spectral operators

TL;DR

This paper explores spectral features of scalar type spectral operators, demonstrating that key properties known for bounded cases extend to unbounded operators in separable spaces, enhancing understanding of their spectral structure.

Contribution

The paper shows that important spectral properties of bounded scalar type spectral operators also hold for unbounded operators in separable spaces, extending existing theory.

Findings

Residual spectrum is empty for these operators.

Point spectrum is countable in separable spaces.

Spectral gap at zero is characterized for unbounded operators.

Abstract

Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at $0$, known to hold for bounded scalar type spectral operators, are shown to naturally transfer to the unbounded case.