In this paper,we introduce the harmonic Hardy space on Tn and study some algebraic properties of dual Toeplitz operator on the harmonic Hardy space on Tn.
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
Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang's results co...Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang's results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang's 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang's paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang's 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ∈ C in an essentially semi-regular domain.展开更多
The(U+K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as(U+K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the(U+...The(U+K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as(U+K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the(U+K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρF(T)}andσp(T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed(U+K)-orbit if they have the same spectral picture,and describe the closures of the(U+K)-orbits of these operator models.These generalize some known results on the closures of(U+K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article"A survey of(U+K)-orbits".展开更多
In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞, as |x|→∞,and the relativistic co...In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞, as |x|→∞,and the relativistic corrections to it,（-△+m<sup>2</sup>）<sup>1/2</sup>+v（x）,v（x）→-∞,as|x|→∞.展开更多
An extension of slant Hankel operator,namely,the kth-orderλ-slant Hankel operator on the Lebesgue space L^(2)(T^(n)),where T is the unit circle and n≥1,a natural number,is described in terms of the solution of a sys...An extension of slant Hankel operator,namely,the kth-orderλ-slant Hankel operator on the Lebesgue space L^(2)(T^(n)),where T is the unit circle and n≥1,a natural number,is described in terms of the solution of a system of operator equations,which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator.The study is further lifted in Calkin algebra in terms of essentially kth-orderλ-slant Hankel operators on L^(2)(T^(n)).展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1167106511301047)
文摘In this paper,we introduce the harmonic Hardy space on Tn and study some algebraic properties of dual Toeplitz operator on the harmonic Hardy space on Tn.
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 No.11171066)Specialized Research Fund for the Doctoral Program of Higher Education (Grant Nos. 2010350311001 and 20113503120003)+1 种基金Natural Science Foundation of Fujian Province (Grant Nos. 2011J05002 and 2012J05003)Foundation of the Education Department of Fujian Province (Grant No. JB10042)
文摘Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang's results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang's 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang's paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang's 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ∈ C in an essentially semi-regular domain.
基金supported by National Natural Science Foundation of China(Grant Nos.10701031,10571041)
文摘The(U+K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as(U+K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the(U+K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρF(T)}andσp(T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed(U+K)-orbit if they have the same spectral picture,and describe the closures of the(U+K)-orbits of these operator models.These generalize some known results on the closures of(U+K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article"A survey of(U+K)-orbits".
文摘In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞, as |x|→∞,and the relativistic corrections to it,（-△+m<sup>2</sup>）<sup>1/2</sup>+v（x）,v（x）→-∞,as|x|→∞.
文摘An extension of slant Hankel operator,namely,the kth-orderλ-slant Hankel operator on the Lebesgue space L^(2)(T^(n)),where T is the unit circle and n≥1,a natural number,is described in terms of the solution of a system of operator equations,which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator.The study is further lifted in Calkin algebra in terms of essentially kth-orderλ-slant Hankel operators on L^(2)(T^(n)).
