Unbounded Products of Operators and Connections to Dirac-Type Operators

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 $\overline{AB}$ 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.

17 pages

References in corpus (3)

• Abstract Wave Equations and Associated Dirac-Type Operators
• The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness and Normality
• Products of Unbounded Normal Operators

Cited by in corpus (3)

• On Selfadjoint Spectral Theory of Random Operators
• Conditions Implying Commutativity of Unbounded Self-adjoint Operators and Related Topics
• Commutativity up to a factor for bounded and unbounded operators