In [1—3], we have discussed problems on the Putnam-Fuglede theorem of non-normal operators which reduce AX=XB’（AXB=X） to A*X =XB* （A*XB* =X）. For the normal operators the following problems are considered: Let ...In [1—3], we have discussed problems on the Putnam-Fuglede theorem of non-normal operators which reduce AX=XB’（AXB=X） to A*X =XB* （A*XB* =X）. For the normal operators the following problems are considered: Let （N1, …,Nn） and （M1,…, Mn） be two groups of commuting normal operators, and we展开更多
During the last fifteen years, there have been many attempts to study the noncasual stochastic integrals and the related calculus, which have been made a very significant progress in stochastic analysis. Up to now, mo...During the last fifteen years, there have been many attempts to study the noncasual stochastic integrals and the related calculus, which have been made a very significant progress in stochastic analysis. Up to now, most of them are devoted to anticipating stochastic integrals with respect to Wiener process, and there is no unified theory of stochastic integrals. By Gaussian operators, we consider the Skorohod integrals with respect to random fields. These results would be used to study stochastic differential equations with ’noise fields’.展开更多
In the Pontrjagin space π_K, there is a basic result that for any unitary (or self adjoint) operator, there exists a non-positive K-dimensional invariant subspace. For a self adjoint operator A on Krien space π, if ...In the Pontrjagin space π_K, there is a basic result that for any unitary (or self adjoint) operator, there exists a non-positive K-dimensional invariant subspace. For a self adjoint operator A on Krien space π, if π=H_-⊕_+ is a regular decomposition of π, and P_-AP_+ is a compact operator, then there exists a maximum non-positive in-展开更多
In this paper, Π denotes Krein space, (·,·) denotes the infinitive inner product. The Π-type spaces refer to the Pontrjagin spaces or Krein spaces. The Hilbert spaces are also regarded as Π-type spaces. T...In this paper, Π denotes Krein space, (·,·) denotes the infinitive inner product. The Π-type spaces refer to the Pontrjagin spaces or Krein spaces. The Hilbert spaces are also regarded as Π-type spaces. The chief aim of this paper is to discuss the structure of the Π space. Definition 1. Let L be a closed subspace of Π. L is called a complete subspaee of Π if it is also a Π-type space according to (·,·).展开更多
Let H be a complex Hilbert space, B（H） the set of bounded linear operators on H, C the complex field. For any A, A-1∈B（H）, the operator C=A*-1A is called polar-product operator of A in (1)The properties of C were...Let H be a complex Hilbert space, B（H） the set of bounded linear operators on H, C the complex field. For any A, A-1∈B（H）, the operator C=A*-1A is called polar-product operator of A in (1)The properties of C were studied in (1)In [2], we have used the polar-product to show the solvability of the operator equation λA2+μA*2=αA*A+βAA*（λ, μ, α, β∈C）, and given all its solutions. On discus-展开更多
Given an r-discrete, principal and amenable groupoid, the bijective correspondence between the family c the closedC o(G 0)-bimodules ofC(G) and the family of the open subsets of the groupoidG is established. More over...Given an r-discrete, principal and amenable groupoid, the bijective correspondence between the family c the closedC o(G 0)-bimodules ofC(G) and the family of the open subsets of the groupoidG is established. More over they are rigidity.展开更多
Let π_k be a Pontrjagin space, which has a maximal seminegative subspace with k dimensions, and (.,.) be the indefinite inner product on π_k. A linear bounded operator T is called a contraction, if (Tx, Tx)≤(x, x )...Let π_k be a Pontrjagin space, which has a maximal seminegative subspace with k dimensions, and (.,.) be the indefinite inner product on π_k. A linear bounded operator T is called a contraction, if (Tx, Tx)≤(x, x ) for any x∈π_k.展开更多
The structure of the groupoid G associated with the Toeplitz C* -algebra C*(Ω) of the L-shaped domain is discussed. The detailed characterization of M∞ by the classification of the closed subgroup of the Euclidean s...The structure of the groupoid G associated with the Toeplitz C* -algebra C*(Ω) of the L-shaped domain is discussed. The detailed characterization of M∞ by the classification of the closed subgroup of the Euclidean space is presented.展开更多
The concept of the regular contractions was introduced in [1], and it was proved that there must be the unitary dilations for regular contractions in Halmos or Nagy sense, consequently, the conjugate operator of a reg...The concept of the regular contractions was introduced in [1], and it was proved that there must be the unitary dilations for regular contractions in Halmos or Nagy sense, consequently, the conjugate operator of a regular contraction is also a展开更多
In this paper we are to discuss the general form of the unitary dilation of the operator on the Hilbert space or on the space with an indefinite metric.Let H be a Hilbert space, and T be a contraction （or bounded ope...In this paper we are to discuss the general form of the unitary dilation of the operator on the Hilbert space or on the space with an indefinite metric.Let H be a Hilbert space, and T be a contraction （or bounded operator） on H. If there are two Hilbert spaces H1, H2 （or two spaces with indefinite metric, Ji is the metric operator of Hi, i=1, 2） and a unitary operator (or relative to the展开更多
§ 1. IntroductionIn Krein space H, the following results were proved in [1]: suppose that U is a unitary operator in H, and there exists a polynomial p(*) such that p(U} is quasi-nilpotent, then ([1], Theorem 2 (...§ 1. IntroductionIn Krein space H, the following results were proved in [1]: suppose that U is a unitary operator in H, and there exists a polynomial p(*) such that p(U} is quasi-nilpotent, then ([1], Theorem 2 (ii)) there exists a decomposition n = ^@IIlt展开更多
文摘In [1—3], we have discussed problems on the Putnam-Fuglede theorem of non-normal operators which reduce AX=XB’（AXB=X） to A*X =XB* （A*XB* =X）. For the normal operators the following problems are considered: Let （N1, …,Nn） and （M1,…, Mn） be two groups of commuting normal operators, and we
基金Project partially supported by the National Natural Science Foundation of China.
文摘During the last fifteen years, there have been many attempts to study the noncasual stochastic integrals and the related calculus, which have been made a very significant progress in stochastic analysis. Up to now, most of them are devoted to anticipating stochastic integrals with respect to Wiener process, and there is no unified theory of stochastic integrals. By Gaussian operators, we consider the Skorohod integrals with respect to random fields. These results would be used to study stochastic differential equations with ’noise fields’.
文摘In the Pontrjagin space π_K, there is a basic result that for any unitary (or self adjoint) operator, there exists a non-positive K-dimensional invariant subspace. For a self adjoint operator A on Krien space π, if π=H_-⊕_+ is a regular decomposition of π, and P_-AP_+ is a compact operator, then there exists a maximum non-positive in-
文摘In this paper, Π denotes Krein space, (·,·) denotes the infinitive inner product. The Π-type spaces refer to the Pontrjagin spaces or Krein spaces. The Hilbert spaces are also regarded as Π-type spaces. The chief aim of this paper is to discuss the structure of the Π space. Definition 1. Let L be a closed subspace of Π. L is called a complete subspaee of Π if it is also a Π-type space according to (·,·).
文摘Let H be a complex Hilbert space, B（H） the set of bounded linear operators on H, C the complex field. For any A, A-1∈B（H）, the operator C=A*-1A is called polar-product operator of A in (1)The properties of C were studied in (1)In [2], we have used the polar-product to show the solvability of the operator equation λA2+μA*2=αA*A+βAA*（λ, μ, α, β∈C）, and given all its solutions. On discus-
文摘Given an r-discrete, principal and amenable groupoid, the bijective correspondence between the family c the closedC o(G 0)-bimodules ofC(G) and the family of the open subsets of the groupoidG is established. More over they are rigidity.
文摘Let π_k be a Pontrjagin space, which has a maximal seminegative subspace with k dimensions, and (.,.) be the indefinite inner product on π_k. A linear bounded operator T is called a contraction, if (Tx, Tx)≤(x, x ) for any x∈π_k.
基金Project supported partially by the National Natural Science Foundation of China,Fok Yingtung Educational Foundation and the Foundation of the Stare Education Commission of China.
文摘The structure of the groupoid G associated with the Toeplitz C* -algebra C*(Ω) of the L-shaped domain is discussed. The detailed characterization of M∞ by the classification of the closed subgroup of the Euclidean space is presented.
文摘The concept of the regular contractions was introduced in [1], and it was proved that there must be the unitary dilations for regular contractions in Halmos or Nagy sense, consequently, the conjugate operator of a regular contraction is also a
文摘In this paper we are to discuss the general form of the unitary dilation of the operator on the Hilbert space or on the space with an indefinite metric.Let H be a Hilbert space, and T be a contraction （or bounded operator） on H. If there are two Hilbert spaces H1, H2 （or two spaces with indefinite metric, Ji is the metric operator of Hi, i=1, 2） and a unitary operator (or relative to the
文摘§ 1. IntroductionIn Krein space H, the following results were proved in [1]: suppose that U is a unitary operator in H, and there exists a polynomial p(*) such that p(U} is quasi-nilpotent, then ([1], Theorem 2 (ii)) there exists a decomposition n = ^@IIlt
