Weighted shifts on directed trees: their multiplier algebras, reflexivity and decompositions
Piotr Budzyński , Piotr Dymek , Artur Płaneta , Marek Ptak
AbstractWe 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.
|Journal series||Studia Mathematica, ISSN 0039-3223, e-ISSN 1730-6337, (N/A 100 pkt)|
|Publication size in sheets||1.15|
|Keywords in English||weighted shift on directed tree, multiplication operator, reflexive algebras, Wold-type decomposition|
|Publication indicators||= 2; : 2017 = 1.076; : 2018 = 0.75 (2) - 2018=0.663 (5)|
|Finansowanie||The second, third and fourth authors were supported by the Ministry of Science and Higher Education of Poland|
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