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arXiv · 1308.2427

Unbounded Products of Operators and Connections to Dirac-Type Operators

Karl Gustafson·Mohammed Hichem Mortad
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Abstract

Let $A$ and $B$ be two densely defined unbounded closeable operators in a Hilbert space such that their unbounded operator products $AB$ and $BA$ are also densely defined. Then all four operators possess adjoints and we obtain new inclusion bounds for the operator product closures $\bar{A} \bar{B}$ and $\bar{AB}$ in terms of new relations among the operator adjoints. These in turn lead to sharpened understandings for when products of unbounded self-adjoint and unbounded normal operators are self-adjoint and normal. They also clarify certain operator-product issues for Dirac operators.

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Karl Gustafson, Mohammed Hichem Mortad. 2013-08-11. Unbounded Products of Operators and Connections to Dirac-Type Operators. https://doi.org/10.1016/j.bulsci.2013.10.007

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