Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(5): 1471-1481

Online first article September 13, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150774

Copyright © The Korean Mathematical Society.

Reducing subspaces of weighted shifts with operator weights

Caixing Gu

California Polytechnic State University

Abstract

We characterize reducing subspaces of weighted shifts with operator weights as wandering invariant subspaces of the shifts with additional structures. We show how some earlier results on reducing subspaces of powers of weighted shifts with scalar weights on the unit disk and the polydisk can be fitted into our general framework.

Keywords: weighted shifts with operator weights, reducing subspaces, analytic Toeplitz operators, Bergman space, bidisk

MSC numbers: Primary 47B37, 47A15