Journal article
The Mean Transform and the Mean Limit of an Operator
Proceedings of the American Mathematical Society, Vol.147(3), pp.1119-1133
03/01/2019
DOI: 10.1090/proc/14277
Abstract
Let T ε B(H) be a bounded linear operator on a Hilbert space H, and let T ≡ V |T| be the polar decomposition of T. The mean transform of T is defined by T := 1/2 (V |T| + |T|V) . In this paper we study the iterates of the mean transform and we define the mean limit of an operator as the limit (in the operator norm) of those iterates. We obtain new estimates for the numerical range and numerical radius of the mean transform in terms of the original operator. For the special class of unilateral weighted shifts we describe the precise relationship between the spectral radius and the mean limit, and obtain some sharp estimates.
Details
- Title: Subtitle
- The Mean Transform and the Mean Limit of an Operator
- Creators
- Fadil Chabbabi - Univ Lille, UFR Math, Lab P Painleve, CNRS,UMR 8524, F-59655 Villeneuve Dascq, FranceRaul E. Curto - University of Iowa, MathematicsMostafa Mbekhta - Univ Lille, UFR Math, Lab P Painleve, CNRS,UMR 8524, F-59655 Villeneuve Dascq, France
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.147(3), pp.1119-1133
- DOI
- 10.1090/proc/14277
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Number of pages
- 15
- Grant note
- ANR-11-LABX-0007-01 / Labex CEMPI DMS-1302666 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 03/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9983985971602771
Metrics
30 Record Views