NDLI: On the Aluthge Transforms of Weighted Shifts with Moments of Fibonacci Type. Application to Subnormality

Content Provider	Springer Nature Link
Author	Ben Taher, R. Rachidi, M. Zerouali, E. H.
Copyright Year	2015
Abstract	In this paper, we investigate the properties of the Aluthge transforms of weighted shifts whose moment sequence is a generalized Fibonacci sequence of order r (or of Fibonacci type). We provide sufficient conditions under which the Aluthge transform has also a moment sequence of Fibonacci type. Notably, we detail the case when the moment sequence is a generalized Fibonacci sequence of order r ≤ 4. This allows us to recover the main result given by S. H. Lee et al. concerning the subnormality of Aluthge transforms of weighted shifts with two atomic Berger measure. We end this paper by considering the extended case of the subnormal weighted shift of a finite atomic Berger measure, with a view to whether its Aluthge transforms is again subnormal. As a result, we give a negative answer to a recent conjecture posed by S. H. Lee et al. in its general setting. Even so, under some mild assumptions we give a positive answer to this conjecture.
Ending Page	299
Page Count	13
Starting Page	287
File Format	PDF
ISSN	0378620X
e-ISSN	14208989
Journal	Integral Equations and Operator Theory
Issue Number	2
Volume Number	82
Language	English
Publisher	Springer Basel
Publisher Date	2015-04-08
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Binet formula subnormal operator Analysis generalized Fibonacci sequence The Aluthge transforms Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) Moment problems Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) representing measure subnormal weighted shift
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Analysis

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