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July, 2018 Common reducing subspaces of several weighted shifts with operator weights
Caixing GU
J. Math. Soc. Japan 70(3): 1185-1225 (July, 2018). DOI: 10.2969/jmsj/74677467


We characterize common reducing subspaces of several weighted shifts with operator weights. As applications, we study the common reducing subspaces of the multiplication operators by powers of coordinate functions on Hilbert spaces of holomorphic functions in several variables. The identification of reducing subspaces also leads to structure theorems for the commutants of von Neumann algebras generated by these multiplication operators. This general approach applies to weighted Hardy spaces, weighted Bergman spaces, Drury–Arveson spaces and Dirichlet spaces of the unit ball or polydisk uniformly.


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Caixing GU. "Common reducing subspaces of several weighted shifts with operator weights." J. Math. Soc. Japan 70 (3) 1185 - 1225, July, 2018.


Received: 16 March 2016; Revised: 31 January 2017; Published: July, 2018
First available in Project Euclid: 25 June 2018

zbMATH: 06966980
MathSciNet: MR3830805
Digital Object Identifier: 10.2969/jmsj/74677467

Primary: 47A15 , 47B35 , 47B37
Secondary: 32A35‎ , ‎32A36‎ , 46E22

Keywords: analytic Toeplitz operators , Dirichlet space on polydisk , reducing subspaces , weighted Bergman spaces , weighted Hardy space on unit ball , weighted shifts with operator weights

Rights: Copyright © 2018 Mathematical Society of Japan


Vol.70 • No. 3 • July, 2018
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