Weighted shifts on directed trees: their multiplier algebras, reflexivity and decompositions

Piotr Budzyński , Piotr Dymek , Artur Płaneta , Marek Ptak

Abstract

We study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the weighted shift. From this fact we deduce reflexivity of those weighted shifts on rooted directed trees whose all path-induced spectral-like radii are positive. We show that weighted shifts with positive weights on rooted directed trees admit a Wold-type decomposition. We prove that the pairwise orthogonality of the factors in the decomposition is equivalent to the weighted shift being balanced.
Author Piotr Budzyński (FoEEaLS / DoAM)
Piotr Budzyński,,
- Department of Applied Mathematics
, 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 seriesStudia Mathematica, ISSN 0039-3223, e-ISSN 1730-6337, (N/A 100 pkt)
Issue year2019
Vol244
No3
Pages285-308
Publication size in sheets1.15
Keywords in Englishweighted shift on directed tree, multiplication operator, reflexive algebras, Wold-type decomposition
ASJC Classification2600 General Mathematics
DOIDOI:10.4064/sm170220-20-9
URL https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/online/101501/weighted-shifts-on-directed-trees-their-multiplier-algebras-reflexivity-and-decompositions
Internal identifierWIŚIG/2019/1
Languageen angielski
Score (nominal)100
Score sourcejournalList
Publication indicators WoS Citations = 2; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.076; WoS Impact Factor: 2018 = 0.75 (2) - 2018=0.663 (5)
Citation count*
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FinansowanieThe second, third and fourth authors were supported by the Ministry of Science and Higher Education of Poland
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