Given a pair of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for the existence of a commuting pair of normal extensions of and ; in other words, is a subnormal pair. The LPCS is a longstanding open problem in the operator theory. In this paper, we consider the LPCS of a class of powers of -variable weighted shifts. Our main theorem states that if a “corner” of a 2-variable weighted shift is subnormal, then is subnormal if and only if a power is subnormal for some . As a corollary, we have that if is a 2-variable weighted shift having a tensor core or a diagonal core, then is subnormal if and only if a power of is subnormal.
Lee, S. H., Lee, W. Y., & Yoon, J. (2020). Subnormality of Powers of Multivariable Weighted Shifts. Journal of Function Spaces, 2020, 5678795. https://doi.org/10.1155/2020/5678795
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Journal of Function Spaces