Journal article
The Aluthge transform of unilateral weighted shifts and the Square Root Problem for finitely atomic measures
Mathematische Nachrichten, Vol.292(11), pp.2352-2368
11/01/2019
DOI: 10.1002/mana.201800140
Abstract
In this paper we consider the following Square Root Problem for measures: Given a positive probability Borel measure mu (supported on an interval [a,b]subset of R+), does there exist a positive Borel measure nu such that mu=nu*nu holds? (Here * denotes the multiplicative convolution, properly defined on R+.) This problem is intimately connected to the subnormality of the Aluthge transform of a unilateral weighted shift. We develop a criterion to test whether a measure mu admits a square root, and we provide a concrete solution for the case of a finitely atomic measure having at most five atoms. In addition, we sharpen the statement of a previous result on this topic and extend its applicability via a new technique that uses the standard inequality of real numbers to generate a diagram of a partial order on the support of a probability measure.
Details
- Title: Subtitle
- The Aluthge transform of unilateral weighted shifts and the Square Root Problem for finitely atomic measures
- Creators
- Raul E Curto - University of IowaJaewoong Kim - Korea Military AcademyJasang Yoon - The University of Texas Rio Grande Valley
- Resource Type
- Journal article
- Publication Details
- Mathematische Nachrichten, Vol.292(11), pp.2352-2368
- DOI
- 10.1002/mana.201800140
- ISSN
- 0025-584X
- eISSN
- 1522-2616
- Publisher
- WILEY-V C H VERLAG GMBH
- Number of pages
- 17
- Grant note
- University of Texas System NSF; National Science Foundation (NSF) DMS-1302666 / Division of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) CONACYT; Consejo Nacional de Ciencia y Tecnologia (CONACyT) 2018(18-MS-10) / Korea Military Academy 2016R1D1A1A09918018 / National Research Foundation of Korea; National Research Foundation of Korea
- Language
- English
- Date published
- 11/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984240863002771
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