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.
