School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Recursiveness and propagation for 2-variable weighted shifts
Document Type
Article
Publication Date
9-2006
Abstract
For 1-variable weighted shifts, it is well known that given three positive numbers α0<α1<α2 , we always find Stampfli's subnormal weighted shift whose first three weights are α0 , α1 and α2 (we call it a type-abc completion, or shift.) On the other hand, given four positive numbers α0<α1<α2<α3 , it is not always possible to find a subnormal weighted shift whose first four weights are α0 , α1 , α2 and α3 . In this paper, we extend the notion of a type-abc shift to the 2-variable weighted shifts using a localization technique from the theory of truncated moment problems. We next study an inner propagation phenomena of a 2-variable weighted shift whose core is of type-abc. We further establish the necessary and sufficient conditions for the subnormality of one-step extensions of type-abc 2-variable weighted shifts. Finally, we study a certain invariant property under powers for type-abc 2-variable weighted shifts.
Recommended Citation
Lee, Sang Hoon, and Jasang Yoon. "Recursiveness and propagation for 2-variable weighted shifts." Linear Algebra and its Applications 504 (2016): 228-247. https://doi.org/10.1016/j.laa.2016.04.006
Publication Title
Linear Algebra and its Applications
DOI
10.1016/j.laa.2016.04.006
Comments
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