Operator analogues of Mahler's measure
Functional Analysis
2013-12-19 v1 Number Theory
Abstract
Motivated by a geometric meaning of Mahler's measure, we introduce two operator analogues of Mahler's measure. This leads to some interesting equalities and inequalities between the two operator-theoretic Mahler measures and the classical Mahler measure. In order to apply these results to the operator version of Lehmer's problem, we introduce and study an important class of operators, the so-called subharmonic operators. It is shown that the operator version of Lehmer's problem fails under some mild condition.
Keywords
Cite
@article{arxiv.1312.4247,
title = {Operator analogues of Mahler's measure},
author = {Kunyu Guo and Jiayang Yu},
journal= {arXiv preprint arXiv:1312.4247},
year = {2013}
}
Comments
This article has been accepted by the llinois Journal of Mathematics