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Subnormality of Powers of Multivariable Weighted Shifts.
- Source :
-
Journal of Function Spaces . 11/28/2020, p1-11. 11p. - Publication Year :
- 2020
-
Abstract
- Given a pair T ≡ T 1 , T 2 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 N ≡ N 1 , N 2 of normal extensions of T 1 and T 2 ; in other words, T 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 2 -variable weighted shifts. Our main theorem states that if a "corner" of a 2-variable weighted shift T = W α , β ≔ T 1 , T 2 is subnormal, then T is subnormal if and only if a power T m , n ≔ T 1 m , T 2 n is subnormal for some m , n ≥ 1. As a corollary, we have that if T is a 2-variable weighted shift having a tensor core or a diagonal core, then T is subnormal if and only if a power of T is subnormal. [ABSTRACT FROM AUTHOR]
- Subjects :
- *OPERATOR theory
*HILBERT space
Subjects
Details
- Language :
- English
- ISSN :
- 23148896
- Database :
- Academic Search Index
- Journal :
- Journal of Function Spaces
- Publication Type :
- Academic Journal
- Accession number :
- 147265260
- Full Text :
- https://doi.org/10.1155/2020/5678795