共查询到20条相似文献,搜索用时 406 毫秒
1.
Palle E.T. Jorgensen 《Journal of Functional Analysis》1979,34(1):138-145
We prove a commutation theorem for point ultraweakly continuous oneparameter groups of automorphisms of von Neumann algebras. If αt, is such a group in Aut() for a von Neumann algebra , we show the equivalence of the following three conditions on an ultraweakly continuous linear transformation μ: → : (a) μ commutes weakly with the infinitesimal generator for αt; (b) μ ° αt = αt ° μ, t ∈ R; and (c) μ leaves invariant each of the spectral subspaces associated with αt. A simple condition which is applicable when μ is an automorphism is pointed out. 相似文献
2.
Thomas G Kurtz 《Journal of Functional Analysis》1973,12(1):55-67
Let U(t) and S(t) be strongly continuous contraction semigroups on a Banach space L with infinitesimal operators A and B, respectively. Suppose the closure of A + αB generates a semigroup Tα(t). The behavior of Tα(t) as α goes to infinity is examined. In particular, suppose S(t) converges strongly to P. If the closure of PA generates a semigroup T(t) on (P), then Tα(t) goes to T(t) on (P). If PA = 0 and if BVf = ?f for fε(P), conditions are given that imply Tα(αt) converges on (P) to a semigroup generated by the closure of PAVA.The results are used to obtain new and known limit theorems for random evolutions, which in turn give approximation theorems for diffusion processes. 相似文献
3.
John Palmer 《Journal of Functional Analysis》1978,27(3):308-336
In this paper a Cohen factorization theorem x = at · xt (t > 0) is proved for a Banach algebra A with a bounded approximate identity, where t ? at is a continuous one-parameter semigroup in A. This theorem is used to show that a separable Banach algebra B has a bounded approximate identity bounded by 1 if and only if there is a homomorphism θ from L1(+) into B such that ∥ θ ∥ = 1 and θ(L1(+)). B = B = B · θ(L1(+)). Another corollary is that a separable Banach algebra with bounded approximate identity has a commutative bounded approximate identity, which is bounded by 1 in an equivalent algebra norm. 相似文献
4.
Justin Peters 《Journal of Functional Analysis》1984,59(3):498-534
Given a C1-algebra and endomorphim α, there is an associated nonselfadjoint operator algebra + Xα, called the semi-crossed product of with α. If α is an automorphim, + Xα can be identified with a subalgebra of the C1-crossed product + Xα. If is commutative and α is an automorphim satisfying certain conditions, + Xα is an operator algebra of the type studied by Arveson and Josephson. Suppose S is a locally compact Hausdorff space, φ: S → S is a continuous and proper map, and α is the endomorphim of U=C0(S) given by α(?) = ? ō φ. Necessary and sufficient conditions on the map φ are given to insure that the semi-crossed product Z+XαC0(S) is (i) semiprime; (ii) semisimple; (ii) strongly semisimple. 相似文献
5.
Loren D. Pitt 《Journal of multivariate analysis》1978,8(1):45-54
For Gaussian vector fields {X(t) ∈ Rn:t ∈ Rd} we describe the covariance functions of all scaling limits Y(t) = limα↓0 B?1(α) X(αt) which can occur when B(α) is a d × d matrix function with B(α) → 0. These matrix covariance functions are found to be homogeneous in the sense that for some matrix L and each α > 0, . Processes with stationary increments satisfying (1) are further analysed and are found to be natural generalizations of Lévy's multiparameter Brownian motion. 相似文献
6.
Joel Anderson 《Journal of Functional Analysis》1979,31(2):195-217
Three main results are obtained: (1) If is an atomic maximal Abelian subalgebra of (), is the projection of () onto and h is a complex homomorphism on , then h ° is a pure state on (). (2) If {Pn} is a sequence of mutually orthogonal projections with rank(Pn) = n and ∑ Pn = I, is the projection of () onto {Pn}″ given by P(T)=∑tracen(T)Pn and h is a homomorphism on {Pn}″ such that h(Pn) = 0 for all n then h ° induces a type II∞ factor representation of the Calkin algebra. (3) If is a nonatomic maximal Abelian subalgebra of () then there is an atomic maximal Abelian subalgebra of () and a large family {Φα} of 1-homomorphisms from onto such that for each α, Φα ° is an extreme point in the set of projections from () onto . (Here denotes the projection of () onto .) 相似文献
7.
We consider unbounded derivations in C1-algebras commuting with compact groups of 1-automorphisms. A closed 1-derivation δ in a C1-algebra is said to be a generator if there exists a strongly continuous one-parameter subgroup t∈→τ(t)? Aut() such that . If δ is known to commute with a compact abelian action α:G→Aut(), and if δ(a) = 0 for all a in the fixed point algebra α of the action G, then we show that δ is necessarily a generator. Moreover, in any faithful G-covariant representation, there is a commutative operator field γ ∈ ? → v(γ) such that is possibly unbounded but affiliated with the center of {α}″, and etδ(x) = xetv(γ) for all x in the Arveson spectral subspace α(γ). In particular, if is the CAR algebra over an infinite-dimensional Hilbert space and α is the gauge group, then any such derivation δ is a scalar multiple of the generator of the gauge group. 相似文献
8.
A weighted translation semigroup {St} on L2(+) is defined by for x ? t and 0 otherwise, where φ is a continuous nonzero scalar-valued function on +. It is shown that {St} is subnormal if and only if φ2 is the product of an exponential function and the Laplace-Stieltjes transform of an increasing function of total variation one. A necessary and sufficient condition for similarity of weighted translation semigroups is developed. 相似文献
9.
Herbert Halpern 《Journal of Functional Analysis》1980,36(3):313-342
Let be a von Neumann algebra, let σ be a strongly continuous representation of the locally compact abelian group G as 1-automorphisms of . Let M(σ) be the Banach algebra of bounded linear operators on generated by ∝ σtdμ(t) (μ?M(G)). Then it is shown that M(σ) is semisimple whenever either (i) has a σ-invariant faithful, normal, semifinite, weight (ii) σ is an inner representation or (iii) G is discrete and each σt is inner. It is shown that the Banach algebra L(σ) generated by is semisimple if a is an integrable representation. Furthermore, if σ is an inner representation with compact spectrum, it is shown that L(σ) is embedded in a commutative, semisimple, regular Banach algebra with isometric involution that is generated by projections. This algebra is contained in the ultraweakly continuous linear operators on . Also the spectral subspaces of σ are given in terms of projections. 相似文献
10.
Geoffrey Price 《Journal of Functional Analysis》1982,49(2):145-151
Let be a UHF-algebra of Glimm type n∞, and {αg: g?G} a strongly continuous group of 1-automorphisms of product type on , for G compact. Let α be the C1-subalgebra of fixed elements of . We show that any extremal normalized trace on α arises as the restriction of a symmetric product state ? on of the form ? = ?k?1 ω. As an example we classify the extremal traces on α for the case G = SU(n), αg = ?k ? 1 Ad(g). 相似文献
11.
Let 3 be the set of all 3 × 3 unitary matrices, and let A and B be two 3 × 3 complex nor?al matrices. In this note, the authors first give a necessary and sufficient condition for a 3 × 3 doubly stochastic matrix to be orthostochastic and then use this result to consider the structure of the sets (A) = {Diag UAU1 : U ∈ 3} and W(A,B) = {Tr UAU1B: U ∈ 3}, where 1 denotes the transpose conjugate. 相似文献
12.
Let (μt)∞t=0 be a k-variate (k?1) normal random walk process with successive increments being independently distributed as normal N(δ, R), and μ0 being distributed as normal N(0, V0). Let Xt have normal distribution N(μt, Σ) when μt is given, t = 1, 2,….Then the conditional distribution of μt given X1, X2,…, Xt is shown to be normal N(Ut, Vt) where Ut's and Vt's satisfy some recursive relations. It is found that there exists a positive definite matrix V and a constant θ, 0 < θ < 1, such that, for all t?1, where the norm |·| means that |A| is the largest eigenvalue of a positive definite matrix A. Thus, Vt approaches to V as t approaches to infinity. Under the quadratic loss, the Bayesian estimate of μt is Ut and the process {Ut}∞t=0, U0=0, is proved to have independent successive increments with normal N(θ, Vt?Vt+1+R) distribution. In particular, when V0 =V then Vt = V for all t and {Ut}∞t=0 is the same as {μt}∞t=0 except that U0 = 0 and μ0 is random. 相似文献
13.
14.
Derek W Robinson 《Journal of Functional Analysis》1977,24(3):280-290
Let U, V be two strongly continuous one-parameter groups of bounded operators on a Banach space with corresponding infinitesimal generators S, T. We prove the following: ∥Ut, ? Vt ∥ = O(t), t → 0, if and only if U = V; ∥Ut ? Vt∥ = O(tα), t → 0; with 0 ? α ? 1, if and only if , where Ω, P, are bounded operators on such that if and only if has a bounded extension to 1. Further results of this nature are inferred for semigroups, reflexive spaces, Hilbert spaces, and von Neumann algebras. 相似文献
15.
Kichi-Suke Saito 《Journal of Functional Analysis》1982,45(2):177-193
Let G be a compact abelian group with the archimedean totally ordered dual Γ and let be the von Neumann algebra crossed product determined by a finite von Neumann algebra M and a one-parameter group {αγ}γ?Γ of trace preserving 1-automorphisms of M. In this paper, we investigate the structure of invariant subspaces and cocycles for the subalgebra + of consisting of those operators whose spectrum with respect to the dual automorphism group {βg}g?G on is nonnegative. Our main result asserts that if M is a factor, then + is maximal among the σ-weakly closed subalgebras of . 相似文献
16.
Ola Bratteli Frederick M Goodman Palle E.T Jørgensen 《Journal of Functional Analysis》1985,61(3):247-289
Let G be a compact abelian group, and τ an action of G on a C1-algebra , such that τ(γ)τ(γ)1 = τ(0) τ for all , where τ(γ) is the spectral subspace of corresponding to the character γ on G. Derivations δ which are defined on the algebra F of G-finite elements are considered. In the special case δ¦τ = 0 these derivations are characterized by a cocycle on with values in the relative commutant of τ in the multiplier algebra of , and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded. Under various restrictions on G and τ properties of the cocycle are deduced which again give characterizations of δ in terms of decompositions into generators of one-parameter subgroups of τ(G) and approximately inner derivations. Finally, a perturbation technique is devised to reduce the case δ(F) ? F to the case δ(F) ? F and δ¦τ = 0. This is used to show that any derivation δ with D(δ) = F is wellbehaved and, if furthermore G = T1 and δ(F) ? F the closure of δ generates a one-parameter group of 1-automorphisms of . In the case G = Td, d = 2, 3,… (finite), and δ(F) ? F it is shown that δ extends to a generator of a group of 1-automorphisms of the σ-weak closure of in any G-covariant representation. 相似文献
17.
Richard J McGovern 《Journal of Functional Analysis》1977,26(1):89-101
An unbounded 1-derivation δ on a C1-algebra is called approximately bounded if there is an increasing sequence of full matrix subalgebras {n} whose union is dense in the domain of and a sequence {hn} of self-adjoint elements of such that hn implements δ on n for every n, and {∥hn ? Qn(hn)∥} is a bounded sequence where Qn is the canonical conditional expectation of onto n. We prove that a quasi-free derivation on the Canonical Anticommutation Relation algebra is approximately bounded if the self-adjoint operator from which it arises is of finite multiplicity and bounded. We conjecture that all quasi-free derivations are approximately bounded. We also prove that a quasi-free derivation is bounded if and only if the self-adjoint operator from which it arises is of the trace class. 相似文献
18.
Jean-Yves Charbonnel 《Journal of Functional Analysis》1981,41(2):175-203
Let G be a connected solvable Lie group, π a normal factor representation of G and ψ a nonzero trace on the factor generated by G. We denote by (G) the space of C∞ functions on G which are compactly supported. We show that there exists an element u of the enveloping algebra U of the complexification of the Lie algebra of G for which the linear form on (G) is a nonzero semiinvariant distribution on G. The proof uses results about characters for connected solvable Lie groups and results about the space of primitive ideals of the enveloping algebra U. 相似文献
19.
M.P Heble 《Journal of Mathematical Analysis and Applications》1983,93(2):363-384
Given a cocycle a(t) of a unitary group {U1}, ?∞ < t < ∞, on a Hilbert space , such that a(t) is of bounded variation on [O, T] for every T > O, a(t) is decomposed as a(t) = f;t0Usxds + β(t) for a unique x ? , β(t) yielding a vector measure singular with respect to Lebesgue measure. The variance is defined as if existing. For a stationary diffusion process on 1, with Ω1, the space of paths which are natural extensions backwards in time, of paths confined to one nonsingular interval J of positive recurrent type, an information function I(ω) is defined on , based on the paths restricted to the time interval [0, 1]. It is shown that is continuous and bounded on . The shift τt, defines a unitary representation {Ut}. Assuming , dm being the stationary measure defined by the transition probabilities and the invariant measure on J, has a C∞ spectral density function f;. It is then shown that σ2({Ut}, I) = f;(O). 相似文献
20.
Palle E.T. Jørgensen 《Advances in Mathematics》1982,44(2):105-120
Let Ω be an arbitrary open subset of n of finite positive measure, and assume the existence of a subset Λ ? n such that the exponential functions eλ = exp i(λ1x1 + … + λnxn), λ = (λ1,…, λn) ∈ Λ, form an orthonormal basis for with normalized measure. Assume 0 ∈ Λ and define subgroups K and A of (n, +) by K = Λ0 = {γ ∈ n:γ·λ ∈ 2π}, A = {a ∈ n:Ua U1a = }, where Ut is the unitary representation of n on given by Ute = eitλeλ, t ∈ n, λ ∈ Λ, and where is the multiplication algebra of on L2. Assume that A is discrete. Then there is a discrete subgroup D ? A of dimension n, a fundamental domain for D, and finite sets of representers RΛ, RΓ, , each containing 0, RΛ for in K0, and for in A such that Ω is disjoint union of translates of : Ω = ∪a∈RΩ (a + ), neglecting null sets, and Λ = RΛ ⊕ D0. If RΓ is a set of representers for in D, then Γ = RΓ ⊕ K is a translation set for Ω, i.e., Ω ⊕ Γ = n, direct sum, (neglecting null sets). The case A = n corresponds to Ω = , Λ = D0 and Γ = K. This last case corresponds in turn to a function theoretic assumption of Forelli. 相似文献