In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω...In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.展开更多
In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modul...In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modules of H 2 (Dd) are not essentially normal.展开更多
Let H^2(D^2)be the Hardy space over the bidisk D^2,and let Mψ,φ=[(ψ(z)-φ(w))^2]be the submodule generated by(ψ(z)-φ(w))2,whereψ(z)andφ(w)are nonconstant inner functions.The related quotient module is denoted b...Let H^2(D^2)be the Hardy space over the bidisk D^2,and let Mψ,φ=[(ψ(z)-φ(w))^2]be the submodule generated by(ψ(z)-φ(w))2,whereψ(z)andφ(w)are nonconstant inner functions.The related quotient module is denoted by Nψ,φ=H^2(D^2)ΘMψ,φ.In this paper,we give a complete characterization for the essential normality of Nψ,φ.In particular,ifψ(z)=z,we simply write Mψ,φand Nψ,φas Mφand Nφrespectively.This paper also studies compactness of evaluation operators L(0)|Nφand R(0)|Nφ,essential spectrum of compression operator Sz on Nφ,essential normality of compression operators Sz and Sw on Nφ.展开更多
文摘In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.
基金supported by National Natural Science Foundation of China(Grant Nos.11101240and10831007)Laboratory of Mathematics for Nonlinear Science of Fudan UniversityIndependent Innovation Foundation of Shandong University
文摘In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modules of H 2 (Dd) are not essentially normal.
文摘Let H^2(D^2)be the Hardy space over the bidisk D^2,and let Mψ,φ=[(ψ(z)-φ(w))^2]be the submodule generated by(ψ(z)-φ(w))2,whereψ(z)andφ(w)are nonconstant inner functions.The related quotient module is denoted by Nψ,φ=H^2(D^2)ΘMψ,φ.In this paper,we give a complete characterization for the essential normality of Nψ,φ.In particular,ifψ(z)=z,we simply write Mψ,φand Nψ,φas Mφand Nφrespectively.This paper also studies compactness of evaluation operators L(0)|Nφand R(0)|Nφ,essential spectrum of compression operator Sz on Nφ,essential normality of compression operators Sz and Sw on Nφ.
