Generalized multipliers for left-invertible analytic operators and their applications to commutant and reflexivity

Piotr Dymek , Artur Płaneta , Marek Ptak

Abstract

We introduce generalized multipliers for left-invertible analytic operators. We show that they form a Banach algebra and characterize the commutant of such operators in its terms. In the special case, we describe the commutant of balanced weighted shift only in terms of its weights. In addition, we prove two independent criteria for reflexivity of weighted shifts on directed trees.
Author Piotr Dymek (FoEEaLS / DoAM)
Piotr Dymek,,
- Department of Applied Mathematics
, Artur Płaneta (FoEEaLS / DoAM)
Artur Płaneta,,
- Department of Applied Mathematics
, Marek Ptak (FoEEaLS / DoAM)
Marek Ptak,,
- Department of Applied Mathematics
Journal seriesJournal of Functional Analysis, ISSN 0022-1236, e-ISSN 1096-0783, (N/A 140 pkt)
Issue year2019
Vol276
No4
Pages1244-1275
Publication size in sheets1.55
Keywords in EnglishWeighted shift on directed tree, Generalized multiplier, Commutant, Reflexivity
ASJC Classification2603 Analysis
DOIDOI:10.1016/j.jfa.2018.05.002
URL https://www.sciencedirect.com/science/article/pii/S0022123618301770/pdfft?md5=6b24fae16d59530106560dffbd33dfcd&pid=1-s2.0-S0022123618301770-main.pdf
Internal identifierWIŚIG/2019/35
Languageen angielski
Score (nominal)140
Score sourcejournalList
Publication indicators WoS Citations = 2; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 1.59; WoS Impact Factor: 2018 = 1.637 (2) - 2018=1.715 (5)
Citation count*
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FinansowanieAll authors were supported by the Ministry of Science and Higher Education of the Republic of Poland.
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