Logo image
Back
Classes of operators related to subnormal operators
Preprint   Open access

Classes of operators related to subnormal operators

Raúl E Curto and Thankarajan Prasad
arXiv.org
Cornell University
06/12/2024
DOI: 10.48550/arxiv.2406.08319
url
https://doi.org/10.48550/arxiv.2406.08319View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this paper we attempt to lay the foundations for a theory encompassing some natural extensions of the class of subnormal operators, namely the n--subnormal operators and the sub-n--normal operators. We discuss inclusion relations among the above mentioned classes and other related classes, e.g., n--quasinormal and quasi-n--normal operators. We show that sub-n--normality is stronger than n--subnormality, and produce a concrete example of a 3--subnormal operator which is not sub-2--normal. In \cite{CU1}, R.E. Curto, S.H. Lee and J. Yoon proved that if an operator T is subnormal, left-invertible, and such that Tn is quasinormal for some n≤2, then T is quasinormal. in \cite{JS}, P.Pietrzycki and J. Stochel improved this result by removing the assumption of left invertibility. In this paper we consider suitable analogs of this result for the case of operators in the above-mentioned classes. In particular, we prove that the weight sequence of an n--quasinormal unilateral weighted shift must be periodic with period at most n.
Mathematics - Functional Analysis

Details

Metrics

22 Record Views
Logo image