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1.
In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, theC *-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant of certain shift. The result holds in Bergman spacesA 2(Ω) for a wide class of plane domains Ω⊂C, and in Fock spacesA 2(C N),N≧1.  相似文献   

2.
Denote by T(X) the semigroup of full transformations on a set X. For εT(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={αT(X):αε=εα}. It is well known that C(id X )=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id X ) contains all non-invertible transformations in C(id X ).  相似文献   

3.
UniversalC*-algebrasC*(A) exist for certain topological *-algebras called algebras with aC*-enveloping algebra. A Frechet *-algebraA has aC*-enveloping algebra if and only if every operator representation ofA mapsA into bounded operators. This is proved by showing that every unbounded operator representation π, continuous in the uniform topology, of a topological *-algebraA, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through the enveloping pro-C*-algebraE(A) ofA. Given aC*-dynamical system (G,A,α), any topological *-algebraB containingC c (G,A) as a dense *-subalgebra and contained in the crossed productC*-algebraC*(G,A,α) satisfiesE(B) =C*(G,A,α). IfG = ℝ, ifB is an α-invariant dense Frechet *-subalgebra ofA such thatE(B) =A, and if the action α onB ism-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS(ℝ,B,α) satisfiesE(S(ℝ,B,α)) =C*(ℝ,A,α). WhenG is a Lie group, theC -elementsC (A), the analytic elementsC ω(A) as well as the entire analytic elementsC є(A) carry natural topologies making them algebras with aC*-enveloping algebra. Given a non-unitalC*-algebraA, an inductive system of idealsI α is constructed satisfyingA =C*-ind limI α; and the locally convex inductive limit ind limI α is anm-convex algebra with theC*-enveloping algebraA and containing the Pedersen idealK a ofA. Given generatorsG with weakly Banach admissible relationsR, we construct universal topological *-algebraA(G, R) and show that it has aC*-enveloping algebra if and only if (G, R) isC*-admissible.  相似文献   

4.
We consider a family of operators Hγμ(k), k ∈ \mathbbTd \mathbb{T}^d := (−π,π]d, associated with the Hamiltonian of a system consisting of at most two particles on a d-dimensional lattice ℤd, interacting via both a pair contact potential (μ > 0) and creation and annihilation operators (γ > 0). We prove the existence of a unique eigenvalue of Hγμ(k), k ∈ \mathbbTd \mathbb{T}^d , or its absence depending on both the interaction parameters γ,μ ≥ 0 and the system quasimomentum k ∈ \mathbbTd \mathbb{T}^d . We show that the corresponding eigenvector is analytic. We establish that the eigenvalue and eigenvector are analytic functions of the quasimomentum k ∈ \mathbbTd \mathbb{T}^d in the existence domain G ⊂ \mathbbTd \mathbb{T}^d .  相似文献   

5.
We introduce a geometrical property of norm one complemented subspaces ofC(K) spaces which is useful for computing lower bounds on the norms of projections onto subspaces ofC(K) spaces. Loosely speaking, in the dual of such a space ifx* is a w* limit of a net (x a * ) andx*=x*1+x*2 with ‖x*‖=‖x*1‖ + ‖x*2‖, then we measure how efficiently thex a * 's can be split into two nets converging tox*1 andx*2, respectively. As applications of this idea we prove that if for everyε>0,X is a norm (1+ε) complemented subspace of aC(K) space, then it is norm one complemented in someC(K) space, and we give a simpler proof that a slight modification of anl 1-predual constructed by Benyamini and Lindenstrauss is not complemented in anyC(K) space. Research partially supported by a grant of the U.S.-Israel Binational Science Foundation. Research of the first-named author is supported in part by NSF grant DMS-8602395. Research of the second-named author was partially supported by the Fund for the Promotion of Research at the Technion, and by the Technion VPR-New York Metropolitan Research Fund.  相似文献   

6.
We consider a parabolic semilinear problem with rapidly oscillating coefficients in a domain Ωε that is ε-periodically perforated by small holes of size O\mathcal {O}(ε). The holes are divided into two ε-periodical sets depending on the boundary interaction at their surfaces, and two different nonlinear Robin boundary conditions σε(u ε) + εκ m (u ε) = εg (m) ε, m = 1, 2, are imposed on the boundaries of holes. We study the asymptotics as ε → 0 and establish a convergence theorem without using extension operators. An asymptotic approximation of the solution and the corresponding error estimate are also obtained. Bibliography: 60 titles. Illustrations: 1 figure.  相似文献   

7.
In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, theC *-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant of certain shift. The result holds in Bergman spacesA 2(Ω) for a wide class of plane domains Ω?C, and in Fock spacesA 2(C N),N≧1.  相似文献   

8.
LetP andAC be two primary sequences with min{P, AC}≥RLR ,ρ(P) and ρ(AC) be the eigenvalues ofP andAC, respectively. Letf∈C 0 (I, I) be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved thatf has the kneading sequenceK(f)≥(RC) *m *P if λ≥(ρ(P))1/2m, andK(f)>(RC) *m*AC*E for any shift maximal sequenceE if λ>(ρ(AC))1/2m. The value of (ρ(P))1/2m or (ρ(AC))1/2m is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one. Project supported by the National Natural Science Foundation of China  相似文献   

9.
We use regularized semigroups to consider local linear and semilinear inhomogeneous abstract Cauchy problems on a Banach space in a unified way. We show that the inhomogeneous abstract Cauchy problem {fx43-1} has a unique classical solution, for allf εC([0,T], [Im(C)]),x inC(D(A)), if and only ifA generates aC-regularized semigroup of bounded semivariation, and has a strong solution for allf εL 1 ([0,T], [Im(C)]),x εC(D(A)) if and only if theC-regularized semigroup is what we call of bounded super semivariation. This includes locally Lipschitz continuousC-regularized semigroups. We give similar simple sufficient conditions for the semilinear abstract Cauchy problem {fx43-2} to have a unique solution. Well-known results for generators of strongly continuous semigroups, as well as more recent results for Hille-Yosida operators, originally due to Da Prato and Sinestrari, regarding (0.1), are immediate corollaries of our results. Results due to Desch, Schappacher and Zhang, on (0.2), for generators of strongly continuous semigroups, are similarly generalized to Hille-Yosida operators with our approach. This article appeared in the last issue of the Forum. However, due to an error by the Journal Secetary, the Abstract was omitted, and with it the equations which are the focus of the article. We therefore are reprinting the article in its entirety. The Journal Secretary regrets the error.  相似文献   

10.
LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup N ‖Σ j =0N T j g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed.  相似文献   

11.
We show that if 0<ε≦1, 1≦p<2 andx 1, …,x n is a sequence of unit vectors in a normed spaceX such thatE ‖∑ l n εi x l‖≧n 1/p, then one can find a block basisy 1, …,y m ofx 1, …,x n which is (1+ε)-symmetric and has cardinality at leastγn 2/p-1(logn)−1, where γ depends on ε only. Two examples are given which show that this bound is close to being best possible. The first is a sequencex 1, …,x n satisfying the above conditions with no 2-symmetric block basis of cardinality exceeding 2n 2/p-1. This sequence is not linearly independent. The second example is a sequence which satisfies a lowerp-estimate but which has no 2-symmetric block basis of cardinality exceedingCn 2/p-1(logn)4/3, whereC is an absolute constant. This applies when 1≦p≦3/2. Finally, we obtain improvements of the lower bound when the spaceX containing the sequence satisfies certain type-condition. These results extend results of Amir and Milman in [1] and [2]. We include an appendix giving a simple counterexample to a question about norm-attaining operators.  相似文献   

12.
According to a theorem of Tilson [6] any intersection of free submonoids of a free monoid is free. Here we consider intersections of the form {x, y}* ∩ {u, v}*, where x, y, u and v are words in a finitely generated free monoid Σ*, and show that if both the monoids {x, y}* and {u, v}* are of the rank two, then the intersection is a free monoid generated either by (at most) two words or by a regular language of the form β0 + β((γ(1+ δ + ... δt))*ε for some words β0, β, γ, δ and ε, and some integer t≥0. An example is given showing that the latter possibility may occur for each t≥0 with nonempty values of the words.  相似文献   

13.
It is shown that an n × n matrix of continuous linear maps from a pro-C^*-algebra A to L(H), which verifies the condition of complete positivity, is of the form [V^*TijФ(·)V]^n i,where Ф is a representation of A on a Hilbert space K, V is a bounded linear operator from H to K, and j=1,[Tij]^n i,j=1 is a positive element in the C^*-algebra of all n×n matrices over the commutant of Ф(A) in L(K). This generalizes a result of C. Y.Suen in Proc. Amer. Math. Soc., 112(3), 1991, 709-712. Also, a covariant version of this construction is given.  相似文献   

14.
The commutant modulo compacts, or essential commutant, of a reflexive algebra with commutative subspace lattice is a C* algebra which is the sum of the compact operators in L(H) and a C* subalgebra of the core. We give a characterization of the essential commutant of a separably acting CSL algebra in terms of properties of the spectral measure of an operator in the intersection of the essential commutant and the core. This is used to determine some sufficient conditions on the lattice for when the essential commutant is norm generated by the projections it contains.  相似文献   

15.
A Banach space operatorT ɛB(X) is polaroid,T ɛP, if the isolated points of the spectrum ofT are poles of the resolvent ofT. LetPS denote the class of operators inP which have have SVEP, the single-valued extension property. It is proved that ifT is polynomiallyPS andA ɛB(X) is an algebraic operator which commutes withT, thenf(T+A) satisfies Weyl’s theorem andf(T *+A *) satisfiesa-Weyl’s theorem for everyf which is holomorphic on a neighbourhood of σ(T+A).  相似文献   

16.
Let T be a Calderón-Zygmund operator in a “non-homogeneous” space ( , d, μ), where, in particular, the measure μ may be non-doubling. Much of the classical theory of singular integrals has been recently extended to this context by F. Nazarov, S. Treil, and A. Volberg and, independently by X. Tolsa. In the present work we study some weighted inequalities for T*, which is the supremum of the truncated operators associated with T. Specifically, for1<p<∞, we obtain sufficient conditions for the weight in one side, which guarantee that another weight exists in the other side, so that the corresponding Lp weighted inequality holds for T*. The main tool to deal with this problem is the theory of vector-valued inequalities for T* and some related operators. We discuss it first by showing how these operators are connected to the general theory of vector-valued Calderón-Zygmund operators in non-homogeneous spaces, developed in our previous paper [6]. For the Cauchy integral operator C, which is the main example, we apply the two-weight inequalities for C* to characterize the existence of principal values for functions in weighted Lp.  相似文献   

17.
Abstract. Suppose H is a complex Hilbert space, AH (△) denotes the set of all analytic operator functions on  相似文献   

18.
Let T be a C0–contraction on a separable Hilbert space. We assume that IH − T*T is compact. For a function f holomorphic in the unit disk \mathbbD{\mathbb{D}} and continuous on [`(\mathbbD)]\overline{{\mathbb{D}}}, we show that f(T) is compact if and only if f vanishes on s(T)?\mathbbT\sigma(T)\cap{\mathbb{T}}, where σ(T) is the spectrum of T and \mathbbT{\mathbb{T}} the unit circle. If f is just a bounded holomorphic function on \mathbbD{\mathbb{D}}, we prove that f(T) is compact if and only if limn? ¥||Tnf(T)|| = 0\lim\limits_{n\rightarrow \infty}\|T^{n}f(T)\| = 0.  相似文献   

19.
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈ p B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a B(ε) ifB(ε)=T(ε)A(ε)T −1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈ a B(ε) provided thatA(ε)≈ p B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the origin and was first stated by Wasow. Sponsored by the United States Army under Contract No. DAAG29-75-C-0024  相似文献   

20.
Let Ω be a compact Hausdorff space, X a Banach space, C(Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω, X) → Y a bounded linear operator and U #, U # two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π s (C(Ω, X), Y); (β)U # ∈ Π s (C(Ω), Π s (X, Y)); (γ) U # ε Π s (X, Π s (C(Ω), Y)). A general result, [10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C([0, 1], l p ) with values in l 1 satisfies (α), (β) and (γ), which show that the above implication is the best possible result.  相似文献   

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