Conditions Implying Commutativity of Unbounded Self-adjoint Operators and Related Topics

Autor:	Gustafson, K., Mortad, M. H.
Rok vydání:	2015
Předmět:	Mathematics - Functional Analysis Mathematics - Operator Algebras
Druh dokumentu:	Working Paper
Popis:	Let $B$ be a bounded self-adjoint operator and let $A$ be a nonnegative self-adjoint unbounded operator. It is shown that if $BA$ is normal, it must be self-adjoint and so must be $AB$. Commutativity is necessary and sufficient for this result. If $AB$ is normal, it must be self-adjoint and $BA$ is essentially self-adjoint. Although the two problems seem to be alike, two different and quite interesting approaches are used to tackle each one of them. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1509.01571 Zobrazit plný text záznamu View this record from Arxiv