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Indexed by:期刊论文

Date of Publication:2018-04-01

Journal:BANACH JOURNAL OF MATHEMATICAL ANALYSIS

Included Journals:SCIE、Scopus

Volume:12

Issue:2

Page Number:456-480

ISSN No.:1735-8787

Key Words:reducing subspace; Toeplitz operator; Bergman space; bidisk; von Neumann algebra

Abstract:In this paper, we give a uniform characterization for the reducing subspaces for T-phi with the symbol phi(z) = z(k) + z(-l) (k, l is an element of Z(+)(2)) on the Bergman spaces over the bidisk, including the known cases that phi(Z(1), Z(2)) = z(1)(N)z(2)(N) and phi(Z(1), Z(2)) = Z(1)(N) +Z(2)(-M) with N,M is an element of Z(+). Meanwhile, the reducing subspaces for T(z)n(+z)-M (N,M is an element of Z(+)) on the Bergman space over the unit disk are also described. Finally, we state these results in terms of the commutant algebra V*(phi).