Null-orbit reflexive operators
Functional Analysis
2011-01-13 v1 Operator Algebras
Abstract
We introduce and study the notion of null-orbit reflexivity, which is a slight perturbation of the notion of orbit-reflexivity. Positive results for orbit reflexivity and the recent notion of -orbit reflexivity both extend to null-orbit reflexivity. Of the two known examples of operators that are not orbit-reflexive, one is null-orbit reflexive and the other is not. The class of null-orbit reflexive operators includes the classes of hyponormal, algebraic, compact, strictly block-upper (lower) triangular operators, and operators whose spectral radius is not 1. We also prove that every polynomially bounded operator on a Hilbert space is both orbit-reflexive and null-orbit reflexive.
Cite
@article{arxiv.1101.2218,
title = {Null-orbit reflexive operators},
author = {Don Hadwin and Ileana Ionascu and Hassan Yousefi},
journal= {arXiv preprint arXiv:1101.2218},
year = {2011}
}