Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-04-01

Journal: BANACH JOURNAL OF MATHEMATICAL ANALYSIS

Included Journals: Scopus、SCIE

Volume: 12

Issue: 2

Page Number: 456-480

ISSN: 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).