k-拟-*-A(ｎ)算子的性质(英文)

An operator T is called k-quasi-*-A（n） operator, if T^*k|T¹⁺ⁿ|^2/（1+n）T^k ≥T^*k|T^* |²T^k , k ∈ Z, which is a generalization of quasi-*-A（n） operator. In this paper we prove some properties of k-quasi-*-A（n） operator, such as, if T is a k-quasi-*-A（n） operator and N（T ）■N（T^* ）, then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A（n） operator and N（T ）■N（T ）, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.     

On the Spectra!Subspaces of the Non-Normal Operators

In this paper we have proved Theorem 2. Let T be an operator on the Hilbert space II with the single valued extension property, Suppose that for every X in the complex plane, it holds that $||(T-\lambda)f||^2 \leq ||(T-\lambda)^2f||\cdot ||f||,\forall f \in H$ Then for any closed subset \delta of the plane, the spectral subspace ￡_T (\delta) is closed. Theorem 9. Let T and S^* be semi-hyponormal operators and 0 \notin \sigma_p(s). Suppose that there exists an injective operator W with dense range which satisfies TW = WS. Then T and S are normal operators. Theorem 10. Let S be a co-semi-hyponormal operator with the single valued extension property and be not normal. Then there exists f \ne 0 which satisfies ${\sigma _s}(f) \not\subset \sigma (S)$     

An endpoint estimate for maximal multilinear singular integral operators

A weak type endpoint estimate for the maximal multilinear singular integral operator T*Af(x)=supε＞0|(f)(x-y)＞ε (Ω(x-y)/(|x-y|(n 1)))(A(x)-A(y)-▽A(y)(x-y))f(y)dy| is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO(Rn). A regularity condition on Ω which implies an LlogL type estimate of T*A is given.     

Boundedness of the Littlewood—Paley Operator,the Function g（f）,on BMO（T）

Littlewood-Paley operator,the function g(f),is considered as an operator on BMO(T).It is proved that if f∈BMO(T),then g(f)∈BMO(T) and there is a constant C that is independent of f such that ||g(f)||*≤C||f||*.Moreover,we have got the further results.     

Homeomorphic extension of strongly spirallike mappings in C~n

In this paper we consider a proper subclass nA of the full class of spirallike mappings on the Euclidean unit ball Bn in Cn with respect to a given linear operator A. We use the method of subordination chains to obtain an upper growth result for nA , and we obtain various examples of mappings in the same class of normalized biholomorphic mappings on the unit ball Bn in Cn . We also prove that the class nA is compact, while the full class of spirallike mappings with respect to a linear operator need not be compact in dimension n≥2, even when the operator is diagonal. This is one of the motivations for considering the class nA . Finally we prove that if f is a quasiregular strongly spirallike mapping on Bn such that ||[Df(z)]-1 Af(z)|| is uniformly bounded on Bn , then f extends to a homeomorphism of R2n onto itself. In addition, if A + A* = 2aI n for some a 0, this extension is also quasiconformal on R2n .     

On higher analogues of Courant algebroids

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle TM ⊕∧nT*M for an m-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an (n + 1)-vector field π is closed under the higher-order Dorfman bracket iff π is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on ∧nT*M. The graph of an (n+1)-form ω is closed under...     

On Operators Satisfying T＊｜T2｜T≥ T＊｜T＊｜2T

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class denoted by l-＊-A, of operators satisfying T＊｜T2｜T≥ T＊｜T＊｜2T, and we prove the basic properties of these operators. Using these results, we also prove that if T or T＊ ∈l-＊-A, then w（f（T）） = f（w（T））, σea（f（T）） = f（σea（T）） for every f C H（σ（T））, where g（σ（T）） denotes the set of all analytic functions on an open neighborhood of σ（T）.     

THE SUBORDINATION PRINCIPLE AND ITS APPLICATION TO THE GENERALIZED ROPER-SUFFRIDGE EXTENSION OPERATOR

This note is devoted to applying the principle of subordination in order to explore the Roper-Suffridge extension operator and the Pfaltzgraff-Suffridge extension operator with special analytic properties.First,we prove that both the Roper-Suffridge extension operator and the Pfaltzgraff-Suffridge extension operator preserve subordination.As applications,we obtain that if β∈ [0,1],γ∈[0,1/r] and β+γ≤1,then the Roper-Suffridge extension operatorΦ_β,γ（f）(z)=(f（z₁）,(f（z₁     

Hardy-Orlicz 空间到 Bloch-Orlicz 型空间上的复合算子

Let φ be an analytic self-map of D. The composition operator C_φ is the operator defined on H(D) by C_φ(f) = f ? φ. In this paper, we investigate the boundedness and compactness of the composition operator C_φ from Hardy-Orlicz spaces to Bloch-Orlicz type spaces.     

The varieties of Heisenberg vertex operator algebras

For a vertex operator algebra V with conformal vector ω,we consider a class of vertex operator subalgebras and their conformal vectors.They are called semi-conformal vertex operator subalgebras and semiconformal vectors of(V,ω),respectively,and were used to study duality theory of vertex operator algebras via coset constructions.Using these objects attached to(V,ω),we shall understand the structure of the vertex operator algebra(V,ω).At first,we define the set Sc(V,ω)of semi-conformal vectors of V, then we prove that Sc(V,ω)is an affine algebraic variety with a partial ordering and an involution map.Corresponding to each semi-conformal vector,there is a unique maximal semi-conformal vertex operator subalgebra containing it.The properties of these subalgebras are invariants of vertex operator algebras.As an example,we describe the corresponding varieties of semi-conformal vectors for Heisenberg vertex operator algebras.As an application,we give two characterizations of Heisenberg vertex operator algebras using the properties of these varieties.     

Analytic Operator Rings and Analytic J-Self Adjoint Operator Ring

Let A be a linear bounded operator in Hilbert space H with polar respresentation A =J(A^*A)^{1/2} where J^2=I, J^* = J. we use \pho_J(A) to denote the set of all complex \lambda, such that for any $\lambda \in \rho_J(A)$ there exist an bounded inverce R_J(A,\lambda) of (A—\lambda J)and \sigma_J(A)to complement of \rho_J(A). Let S be a closed Cauchy domain, S\supset \sigma_J(A) and f (z) an analytic function on S. We define $f(A)=\frac{1}{2\pi i}\oint\limits_{2s} {f(\zeta ){R_J}(A,\zeta )d\zeta }$, the set of all such f(A)is denoted M. If f(z) be analytic on S and symmetrical for real axis then f(A) is J-self adjoint. The set of all such f(A)is denoted M'. Let A\otimes B = AJB for A, B \in M(or M'). We have Theorem, the ring of functions analytic on S (or analytic symmetrical for real axis on S) is a algebra homomorphism of M (or M'). The constant function 1 or z corresponds to operator J or A^* respectively. Let $M_J={JB|B \in M}$ and $M'_J={JB|B \in M'}$ If the spectrum of (A^*A)^{1/2} is detached, we have Theorem. M_J has common non-trivial reducing subspace and it is true for M_J.     

SOME CONVERGENCE PROBLEMS REGARDING THE FRACTIONAL SCHR?DINGER PROPAGATOR ON NONCOMPACT MANIFOLDS

Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥ 2),complete,noncompact Riemannian manifold M,we prove that if 0 <α <1,s> α/2 and f ∈ H^s(M),then the fractional Schr?dinger propagator e⁽it|L|^α/2)(f)(x)→f(x) a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds.     

The closures of (U+K)-orbits of essentially normal triangular operator models

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∈ρ F (T)} and σ p (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".     

UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by
for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.     

Decomposition and approximation of multivariate functions on the cube

In this paper, we present a decomposition method of multivariate functions. This method shows that any multivariate function f on [0, 1]d is a finite sum of the form ∑jφjψj , where each φj can be extended to a smooth periodic function, each ψj is an algebraic polynomial, and each φjψj is a product of separated variable type and its smoothness is same as f . Since any smooth periodic function can be approximated well by trigonometric polynomials, using our decomposition method, we find that any smooth multivariate function on [0, 1]d can be approximated well by a combination of algebraic polynomials and trigonometric polynomials. Meanwhile, we give a precise estimate of the approximation error.     

Scattering and Symbol of the Unitary Operaters

In this paper,we discuss the problem of Scattering and symbol of the unitary operators.Themain results are(1)if U and V are unitary operators and J is an operator such that UJ-JV is traceclass,thenexists;(2)if T is a unitary operator such thatP_(ac)(U)=I and T is an operator such that T-UTU is trance class,     

ON THE LINEAR APPROXIMATION OPERATOR WHICH HAS ALGEBRAIC PRECISION OF POINTED ORDER

In this paper,we construct an operator which has algebraic precision of pointed order and approximatesto fC[0,1]uniformly on[0,1].     

Banach关于增生算子零点的修正Mann迭代的注

A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given. The work in this paper is an extension and complement of the corresponding result of Kim T.H. and Xu H.K in 2005     

Eigenvalue inequalities for the clamped plate problem of Lν2 operator

The ■ operator is introduced by Xin(2015), which is an important extrinsic elliptic differential operator of divergence type and has profound geometric meaning. In this paper, we extend the ■ operator to a more general elliptic differential operator ■, and investigate the clamped plate problem of the bi-■ operator,which is denoted by ■ on the complete Riemannian manifolds. A general formula of eigenvalues for the ■ operator is established. Applying this formula, we estimate the eigenvalues on the Riemannian manifolds. As some further applications, we establish some eigenvalue inequalities for this operator on the translating solitons with respect to the mean curvature flows, submanifolds of the Euclidean spaces, unit spheres and projective spaces. In particular, for the case of translating solitons, all of the eigenvalue inequalities are universal.     

A solution to Tingley’s problem for isometries between the unit spheres of compact C*-algebras and JB*-triples

Let f : S(E) → S(B) be a surjective isometry between the unit spheres of two weakly compact JB*-triples not containing direct summands of rank less than or equal to 3. Suppose E has rank greater than or equal to 5. Applying techniques developed in JB*-triple theory, we prove that f admits an extension to a surjective real linear isometry T : E → B. Among the consequences, we show that every surjective isometry between the unit spheres of two compact C*-algebras A and B, without assuming any restriction on the rank of their direct summands(and in particular when A = K(H) and B = K(H′)), extends to a surjective real linear isometry from A into B. These results provide new examples of infinite-dimensional Banach spaces where Tingley's problem admits a positive answer.