An answer to a question of A. Lubin: The lifting problem for commuting subnormals
Sang Hoon Lee, Woo Young Lee, Jasang Yoon
TL;DR
This paper addresses the lifting problem for commuting subnormal operators, demonstrating that subnormality of their sum does not ensure the existence of commuting normal extensions, thus highlighting limitations in operator extension theory.
Contribution
It provides a counterexample showing that subnormality of a sum does not imply the existence of commuting normal extensions, advancing understanding of the lifting problem.
Findings
Subnormal sum does not guarantee commuting normal extensions.
Counterexample clarifies limitations in extension theory.
Highlights complexity in the lifting problem for commuting operators.
Abstract
The subnormality for the sum of commuting subnormal operators does not guarantee the existence of commuting normal extensions.
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