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arXiv · 1509.01571

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

K. Gustafson·M. H. Mortad
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Abstract

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.

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K. Gustafson, M. H. Mortad. 2015-09-04. Conditions Implying Commutativity of Unbounded Self-adjoint Operators and Related Topics. https://arxiv.org/abs/1509.01571

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