2018
DOI: 10.1016/j.jmaa.2018.06.062
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Commutants and reflexivity of multiplication tuples on vector-valued reproducing kernel Hilbert spaces

Abstract: Motivated by the theory of weighted shifts on directed trees and its multivariable counterpart, we address the question of identifying commutant and reflexivity of the multiplication d-tuple Mz on a reproducing kernel Hilbert space H of E-valued holomorphic functions on Ω, where E is a separable Hilbert space and Ω is a bounded domain in C d admitting bounded approximation by polynomials. In case E is a finite dimensional cyclic subspace for Mz, under some natural conditions on the B(E)-valued kernel associate… Show more

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Cited by 6 publications
(7 citation statements)
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“…First, we are going to prove thatφ n (m) SOT −→φ(m) for every m ∈ N 0 . Fix e ∈ E and let g = U e. Then by Lemma 1 (i), (15), (6) and (13) we obtain ϕ n (m)e = Mφ n g(m)…”
Section: Generalized Multipliersmentioning
confidence: 97%
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“…First, we are going to prove thatφ n (m) SOT −→φ(m) for every m ∈ N 0 . Fix e ∈ E and let g = U e. Then by Lemma 1 (i), (15), (6) and (13) we obtain ϕ n (m)e = Mφ n g(m)…”
Section: Generalized Multipliersmentioning
confidence: 97%
“…Proof. (i) Fix e ∈ E and let f = U e. Then by (9), (6), and equality N (L) = E we get φ * U e (n) = n k=0φ (k)P E L n−k e =φ(n)e, n ∈ N 0 .…”
Section: Generalized Multipliersmentioning
confidence: 99%
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“…Aronszajn has given a systematic reproducing kernel theory containing the Bergman kernel function [10]. For more details, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”
Section: Introductionmentioning
confidence: 99%