Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm...Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.展开更多
In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized,...In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.展开更多
Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent...Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H^2,where u is a nonconstant inner function.展开更多
In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not h...In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .展开更多
By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint ...By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.展开更多
<正> The composition operators with closed range on H2( Bn) are characterized, and the Frcdholmness of products of Toeplitz and composition operators discussed. Moreover, using composition operators, the spectra...<正> The composition operators with closed range on H2( Bn) are characterized, and the Frcdholmness of products of Toeplitz and composition operators discussed. Moreover, using composition operators, the spectra of Toeplitz operators are studied.展开更多
In this paper, we study some algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space of the unit disk.
The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
基金partly supported by Natural Science Foundation of the Xinjiang Uygur Autonomous Region(2013211A001)
文摘Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.
基金partially supported by NSFC(11771340,11701434,11431011,11471251,11771441)
文摘In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.
基金supported by Hankuk University of Foreign Studies Research Fund
文摘Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H^2,where u is a nonconstant inner function.
基金supported by National Natural Science Foundation of China(Grant No.11271387)Chongqing Natural Sience Foundation(Grant No.2013jjB 0050)Simons Foundation(Grant No.196300)
文摘In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .
基金Supported by NSFC(Grant Nos.11771401 and 11471189)
文摘By using commutative C*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over CN are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.
基金Project supported by the National Natural Science Foundation of China and the Postdoctoral Science Foundation of China.
文摘<正> The composition operators with closed range on H2( Bn) are characterized, and the Frcdholmness of products of Toeplitz and composition operators discussed. Moreover, using composition operators, the spectra of Toeplitz operators are studied.
基金Supported by NSFC(Grant Nos.11471113,11271332 and 11431011)Zhejiang Provincial SFC(Grant Nos.LY14A010013 and LY13A010021)the Fundamental Research Funds for the Central Universities
文摘In this paper, we study some algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space of the unit disk.
文摘The operator equation λMz^-X = XMzk, for k ≥ 2,λ∈ C, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.
