共查询到20条相似文献,搜索用时 31 毫秒
1.
S. Albeverio 《Journal of Functional Analysis》2005,228(1):144-188
Let S be the orthogonal sum of infinitely many pairwise unitarily equivalent symmetric operators with non-zero deficiency indices. Let J be an open subset of R. If there exists a self-adjoint extension S0 of S such that J is contained in the resolvent set of S0 and the associated Weyl function of the pair {S,S0} is monotone with respect to J, then for any self-adjoint operator R there exists a self-adjoint extension such that the spectral parts and RJ are unitarily equivalent. It is shown that for any extension of S the absolutely continuous spectrum of S0 is contained in that one of . Moreover, for a wide class of extensions the absolutely continuous parts of and S are even unitarily equivalent. 相似文献
2.
Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras 总被引:1,自引:0,他引:1
A nonlinear map φ between operator algebras is said to be a numerical radius isometry if w(φ(T−S))=w(T−S) for all T, S in its domain algebra, where w(T) stands for the numerical radius of T. Let and be two atomic nests on complex Hilbert spaces H and K, respectively. Denote the nest algebra associated with and the diagonal algebra. We give a thorough classification of weakly continuous numerical radius isometries from onto and a thorough classification of numerical radius isometries from onto . 相似文献
3.
Dominic Hughes 《Annals of Pure and Applied Logic》2010,161(10):1244-1253
Gentzen’s classical sequent calculus has explicit structural rules for contraction and weakening. They can be absorbed (in a right-sided formulation) by replacing the axiom P,¬P by Γ,P,¬P for any context Γ, and replacing the original disjunction rule with Γ,A,B implies Γ,A∨B.This paper presents a classical sequent calculus which is also free of contraction and weakening, but more symmetrically: both contraction and weakening are absorbed into conjunction, leaving the axiom rule intact. It uses a blended conjunction rule, combining the standard context-sharing and context-splitting rules: Γ,Δ,A and Γ,Σ,B implies Γ,Δ,Σ,A∧B. We refer to this system as minimal sequent calculus.We prove a minimality theorem for the propositional fragment : any propositional sequent calculus S (within a standard class of right-sided calculi) is complete if and only ifS contains (that is, each rule of is derivable in S). Thus one can view as a minimal complete core of Gentzen’s . 相似文献
4.
Singular values, norms, and commutators 总被引:1,自引:0,他引:1
Omar Hirzallah 《Linear algebra and its applications》2010,432(5):1322-1336
Let and Xi, i=1,…,n, be bounded linear operators on a separable Hilbert space such that Xi is compact for i=1,…,n. It is shown that the singular values of are dominated by those of , where ‖·‖ is the usual operator norm. Among other applications of this inequality, we prove that if A and B are self-adjoint operators such that a1?A?a2 and b1?B?b2 for some real numbers and b2, and if X is compact, then the singular values of the generalized commutator AX-XB are dominated by those of max(b2-a1,a2-b1)(X⊕X). This inequality proves a recent conjecture concerning the singular values of commutators. Several inequalities for norms of commutators are also given. 相似文献
5.
Let γ be the Gauss measure on and the Ornstein-Uhlenbeck operator. For every p in [1,∞)?{2}, set , and consider the sector . The main results of this paper are the following. If p is in (1,∞)?{2}, and , i.e., if M is an Lp(γ)uniform spectral multiplier of in our terminology, and M is continuous on , then M extends to a bounded holomorphic function on the sector . Furthermore, if p=1 a spectral multiplier M, continuous on , satisfies the condition if and only if M extends to a bounded holomorphic function on the right half-plane, and its boundary value M(i·) on the imaginary axis is the Euclidean Fourier transform of a finite Borel measure on the real line. We prove similar results for uniform spectral multipliers of second order elliptic differential operators in divergence form on belonging to a wide class, which contains . From these results we deduce that operators in this class do not admit an H∞ functional calculus in sectors smaller than . 相似文献
6.
Jian-Hua Zhang Shan Feng Hong-Xia Li Rui-Hua Wu 《Linear algebra and its applications》2006,418(1):225-233
Let N be a nest on a complex separable Hilbert space H, and τ(N) be the associated nest algebra. In this paper, we prove that every biderivation of τ(N) is an inner biderivation if and only if dim 0+ ≠ 1 or , and that every generalized biderivation of τ(N) is an inner generalized biderivation if dim 0+ ≠ 1 and . 相似文献
7.
Vegard Lima 《Journal of Functional Analysis》2004,210(1):148-170
We prove that a Banach space X has the metric approximation property if and only if , the space of all finite rank operators, is an ideal in , the space of all bounded operators, for every Banach space Y. Moreover, X has the shrinking metric approximation property if and only if is an ideal in for every Banach space Y.Similar results are obtained for u-ideals and the corresponding unconditional metric approximation properties. 相似文献
8.
All-derivable points of operator algebras 总被引:1,自引:0,他引:1
Jun Zhu 《Linear algebra and its applications》2007,427(1):1-5
Let A be an operator subalgebra in B(H), where H is a Hilbert space. We say that an element Z∈A is an all-derivable point of A for the norm-topology (strongly operator topology, etc.) if, every norm-topology (strongly operator topology, etc.) continuous derivable linear mapping φ at Z (i.e. φ(ST)=φ(S)T+Sφ(T) for any S,T∈A with ST=Z) is a derivation. In this paper, we show that every invertible operator in the nest algebra is an all-derivable point of the nest algebra for the strongly operator topology. We also prove that every nonzero element of the algebra of all 2×2 upper triangular matrixes is an all-derivable point of the algebra. 相似文献
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Joachim Toft 《Bulletin des Sciences Mathématiques》2003,127(2):101-132
We study , of all such that for every ?∈C∞0, where denotes the twisted convolution. We prove that certain boundedness for are completely determined of the behaviour for a at origin, for example that , and that if a(0)<∞, then a∈L2∩L∞. We use the results in order to determine wether positive pseudo-differential operators belong to certain Schatten-casses or not. 相似文献
12.
《Advances in Mathematics》2004,182(2):278-306
Let Tα be the translation operator by α in the space of entire functions defined by . We prove that there is a residual set G of entire functions such that for every f∈G and every the sequence is dense in , that is, G is a residual set of common hypercyclic vectors ( functions) for the family . Also, we prove similar results for many families of operators as: multiples of differential operator, multiples of backward shift, weighted backward shifts. 相似文献
13.
Eva A. Gallardo-Gutiérrez 《Journal of Functional Analysis》2003,203(1):27-43
A bounded operator T acting on a Hilbert space is said to be supercyclic if there is a vector such that the projective orbit and is dense in . We use a new method based on a very simple geometric idea that allows us to decide whether an operator is supercyclic or not. The method is applied to obtain the following result: A composition operator acting on the Hardy space whose inducing symbol is a parabolic linear-fractional map of the disk onto a proper subdisk is not supercyclic. This result finishes the characterization of the supercyclic behavior of composition operators induced by linear fractional maps and, thus, completes previous work of Bourdon and Shapiro. 相似文献
14.
Kehe Zhu 《Journal of Functional Analysis》2003,202(2):327-341
For a finite Blaschke product B let TB denote the analytic multiplication operator (also called a Toeplitz operator) on the Bergman space of the unit disk. We show that the defect operators and both map the Bergman space to the Hardy space and the Hardy space to the Dirichlet space. 相似文献
15.
Branko ?urgus 《Discrete Applied Mathematics》2007,155(13):1774-1792
Let S be a finite set with m elements in a real linear space and let JS be a set of m intervals in R. We introduce a convex operator co(S,JS) which generalizes the familiar concepts of the convex hull, , and the affine hull, , of S. We prove that each homothet of that is contained in can be obtained using this operator. A variety of convex subsets of with interesting combinatorial properties can also be obtained. For example, this operator can assign a regular dodecagon to the 4-element set consisting of the vertices and the orthocenter of an equilateral triangle. For two types of families JS we give two different upper bounds for the number of vertices of the polytopes produced as co(S,JS). Our motivation comes from a recent improvement of the well-known Gauss-Lucas theorem. It turns out that a particular convex set co(S,JS) plays a central role in this improvement. 相似文献
16.
O. Guédon G. Paouris 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(1):87
Let 1?p?∞ and be the unit ball of the Schatten trace class of matrices on Cn or on Rn, normalized to have Lebesgue measure equal to one. We prove that
17.
We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C*-algebra . In the process, we prove for every λ∈R and the inequality
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Caixing Gu 《Journal of Functional Analysis》2004,215(1):178-205
Let X be a bounded linear operator on the Hardy space H2 of the unit disk. We show that if is of finite rank for every inner function θ, then X=T?+F for some Toeplitz operator T? and some finite rank operator F on H2. This solves a variant of an open question where the compactness replaces the finite rank conditions. 相似文献
20.
Let K1,…,Kn be (infinite) non-negative matrices that define operators on a Banach sequence space. Given a function f:[0,∞)×…×[0,∞)→[0,∞) of n variables, we define a non-negative matrix and consider the inequality