
TL;DR
This paper characterizes all correct extensions of a densely defined minimal operator in a Hilbert space that have equal domains with their adjoints, especially focusing on normal and formally normal operators, exemplified by the Cauchy-Riemann operator.
Contribution
It provides a comprehensive description of all correct extensions with domain-equality properties for minimal operators, extending previous results to normal and formally normal cases.
Findings
All correct extensions with $D(L)=D(L^*)$ are characterized.
All correct normal extensions of a formally normal operator are described.
The Cauchy-Riemann operator serves as an illustrative example.
Abstract
Let be a densely defined minimal linear operator in a Hilbert space . We prove theorem that if there exists at least one correct extension of with the property , then we can describe all correct extensions with the property . We also prove that if is formally normal and there exists at least one correct normal extension , then we can describe all correct normal extensions of . As an example, the Cauchy-Riemann operator is given.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Algebraic and Geometric Analysis
