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 н be a complex, separable, infinite dimensional Hilbert space, T ε（Ｈ）. （ｕ＋Ｋ）（T） denotes the （ｕ＋ｋ）-orbit of T, i.e., （ｕ＋ｋ）（T） = {R-1TR: R is invertible and of the form unitary plus compact}...Let н be a complex, separable, infinite dimensional Hilbert space, T ε（Ｈ）. （ｕ＋Ｋ）（T） denotes the （ｕ＋ｋ）-orbit of T, i.e., （ｕ＋ｋ）（T） = {R-1TR: R is invertible and of the form unitary plus compact}. Let be an analytic and simply connected Cauchy domain in C and n ε N. A（, n） denotes the class of operators, each of which satisfies （i） T is essentially normal; （ii） σ（T） =, ρF（T） ∩ σ（T） = ; （iii） ind （λ-T） = -n, nul （λ-T） = 0 （λ∈Ω ）. It is proved that given T1, T2 ε A（, n） and ε > 0, there exists a compact operator K with K <ε such that T1 +Kε （ｕ＋ｋ）（T2）. This result generalizes a result of P. S. Guinand and L. Marcoux [6,15]. Furthermore, the authors give a character of the norm closure of （ｕ＋Ｋ）（T）, and prove that for each T ε A（, n）, there exists a compact （SI） perturbation of T whose norm can be arbitrarily small.展开更多
Given an essentially normal operator T with connected spectrum and ind (λ-T)>0 for λ in ρ F(T)∩σ(T) , and a positive number ∈ ,the authors show that theree xists a compact K with ‖K‖&...Given an essentially normal operator T with connected spectrum and ind (λ-T)>0 for λ in ρ F(T)∩σ(T) , and a positive number ∈ ,the authors show that theree xists a compact K with ‖K‖<∈ such that T+K is strongly irreducible.展开更多
We investigate the adjoints of linear fractional composition operators C ? acting on classical Dirichlet space D(B N ) in the unit ball B N of ? N , and characterize the normality and essential normality of C ? on D(B...We investigate the adjoints of linear fractional composition operators C ? acting on classical Dirichlet space D(B N ) in the unit ball B N of ? N , and characterize the normality and essential normality of C ? on D(B N ) and the Dirichlet space modulo constant function D 0(B N ), where ? is a linear fractional map ? of B N . In addition, we also show that for any non-elliptic linear fractional map ? of B N , the composition maps σ o ? and ? o σ are elliptic or parabolic linear fractional maps of B N .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
In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a^2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c > 0, then there is a sequenc...In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a^2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c > 0, then there is a sequence {f_j } of multipliers and a positive number c such that c'P_M ≤sum from j to ( M_(fj)M*_(fj))≤ P_M, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules are p-essentially normal for p > d.展开更多
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 н be a complex, separable, infinite dimensional Hilbert space, T ε（Ｈ）. （ｕ＋Ｋ）（T） denotes the （ｕ＋ｋ）-orbit of T, i.e., （ｕ＋ｋ）（T） = {R-1TR: R is invertible and of the form unitary plus compact}. Let be an analytic and simply connected Cauchy domain in C and n ε N. A（, n） denotes the class of operators, each of which satisfies （i） T is essentially normal; （ii） σ（T） =, ρF（T） ∩ σ（T） = ; （iii） ind （λ-T） = -n, nul （λ-T） = 0 （λ∈Ω ）. It is proved that given T1, T2 ε A（, n） and ε > 0, there exists a compact operator K with K <ε such that T1 +Kε （ｕ＋ｋ）（T2）. This result generalizes a result of P. S. Guinand and L. Marcoux [6,15]. Furthermore, the authors give a character of the norm closure of （ｕ＋Ｋ）（T）, and prove that for each T ε A（, n）, there exists a compact （SI） perturbation of T whose norm can be arbitrarily small.
文摘Given an essentially normal operator T with connected spectrum and ind (λ-T)>0 for λ in ρ F(T)∩σ(T) , and a positive number ∈ ,the authors show that theree xists a compact K with ‖K‖<∈ such that T+K is strongly irreducible.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671141, 10371091)
文摘We investigate the adjoints of linear fractional composition operators C ? acting on classical Dirichlet space D(B N ) in the unit ball B N of ? N , and characterize the normality and essential normality of C ? on D(B N ) and the Dirichlet space modulo constant function D 0(B N ), where ? is a linear fractional map ? of B N . In addition, we also show that for any non-elliptic linear fractional map ? of B N , the composition maps σ o ? and ? o σ are elliptic or parabolic linear fractional maps of B N .
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.
基金supported by the National Natural Science Foundation of China(Nos.11271075,11371096)Shandong Province Natural Science Foundation(No.ZR2014AQ009)the Fundamental Research Funds of Shandong University(No.2015GN017)
文摘In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a^2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c > 0, then there is a sequence {f_j } of multipliers and a positive number c such that c'P_M ≤sum from j to ( M_(fj)M*_(fj))≤ P_M, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules are p-essentially normal for p > d.
