共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Palle E.T Jørgensen 《Journal of Functional Analysis》1982,45(3):341-356
We consider unbounded 1-derivations δ in UHF-C1-algebras A=(∪∞n=1An)?) with dense domain. If ?n:A→An denotes the conditional expectations onto the finite type I factors n, then we introduce a weak-commutativity condition for δ and the sequence (?n). As a consequence of this condition on δ we establish the existence of an extension derivation δ′ which is the infinitesimal generator of a strongly continuous one-parameter group, α: → Aut(), of 1-automorphisms, i.e., for x?D(δ′). Special properties of α (alias δ′) are considered. We show that AF-algebras are associated to proper restrictions δ of derivations δ′ of product type. We then turn to the extendability problem for quasifree derivations in the CAR-algebra. There, extensions δ′ are calculated which generate strongly continuous semigroups of 1-homomorphisms. These semigroups do not extend to one-parameter groups unless the implementing symmetric operator in one-particle space is already self-adjoint. 相似文献
3.
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
4.
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
5.
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
6.
Let H and K be symmetric linear operators on a C1-algebra with domains D(H) and D(K). H is defined to be strongly K-local if implies for A?D(H) ∩ D(K) and ω in the state space of , and H is completely strongly K-local if implies for A ∈ D(H) ∩ D(K) and Ω in the state of , and H is cpmpletely strongly K-local if is -local on U?Mn for all n ? 1, where n is the identity on the n × n matrices Mn. If is abelian then strong locality and complete strong locality are equivalent. The main result states that if τ is a strongly continuous one-parameter group of 1-automorphisms of with generator δ0 and δ is a derivation which commutes with τ and is completely strongly δ0-local then δ generates a group α of 1-automorphisms of . Various characterizations of α are given and the particular case of periodic τ is discussed. 相似文献
7.
Chan-nan Chang 《Journal of Number Theory》1973,5(6):456-476
Let L be a lattice over the integers of a quaternion algebra with center K which is a -adic field. Then the unitary group U(L) equals its own commutator subgroup and is generated by the unitary transvections and quasitransvections contained in it. Let g be a tableau, U(g), U+(g), , T(g) be the corresponding congruence subgroups of order g. Then , and (the subgroup generated by the unitary transvections and quasitransvections with order ≤ g). Let G be a subgroup of U(L) with o(G) = g, then G is normal in U(L) if and only if U(g) ? G ? T(g). 相似文献
8.
Robert L Miller 《Journal of Combinatorial Theory, Series A》1979,26(2):166-178
In this paper we show that two minimal codes 1 and 2 in the group algebra 2[G] have the same (Hamming) weight distribution if and only if there exists an automorphism θ of G whose linear extension to 2[G] maps 1 onto 2. If θ(M1) = M2, then 1 and 2 are called equivalent. We also show that there are exactly τ(l) inequivalent minimal codes in 2[G], where ? is the exponent of G, and τ(?) is the number of divisors of ?. 相似文献
9.
For finite graphs F and G, let NF(G) denote the number of occurrences of F in G, i.e., the number of subgraphs of G which are isomorphic to F. If and are families of graphs, it is natural to ask then whether or not the quantities NF(G), F∈, are linearly independent when G is restricted to . For example, if = {K1, K2} (where Kn denotes the complete graph on n vertices) and is the family of all (finite) trees, then of course NK1(T) ? NK2(T) = 1 for all T∈. Slightly less trivially, if = {Sn: n = 1, 2, 3,…} (where Sn denotes the star on n edges) and again is the family of all trees, then Σn=1∞(?1)n+1NSn(T)=1 for all T∈. It is proved that such a linear dependence can never occur if is finite, no F∈ has an isolated point, and contains all trees. This result has important applications in recent work of L. Lovász and one of the authors (Graham and Lovász, to appear). 相似文献
10.
Hui-Hsiung Kuo 《Journal of Functional Analysis》1976,21(1):63-75
Some parallel results of Gross' paper (Potential theory on Hilbert space, J. Functional Analysis1 (1967), 123–181) are obtained for Uhlenbeck-Ornstein process U(t) in an abstract Wiener space (H, B, i). Generalized number operator is defined by f(x) = ?lim∈←0{E[f((τ∈ξ))] ? f(x)}/E[τ∈ξ, where τx? is the first exit time of U(t) starting at x from the ball of radius ? with center x. It is shown that f(x) = ?trace D2f(x)+〈Df(x),x〉 for a large class of functions f. Let rt(x, dy) be the transition probabilities of U(t). The λ-potential Gλf, λ > 0, and normalized potential Rf of f are defined by Gλf(X) = ∫0∞e?λtrtf(x) dt and Rf(x) = ∫0∞ [rtf(x) ? rtf(0)] dt. It is shown that if f is a bounded Lip-1 function then trace D2Gλf(x) ? 〈DGλf(x), x〉 = ?f(x) + λGλf(x) and trace D2Rf(x) ? 〈DRf(x), x〉 = ?f(x) + ∫Bf(y)p1(dy), where p1 is the Wiener measure in B with parameter 1. Some approximation theorems are also proved. 相似文献
11.
Tom M. Apostol 《Journal of Number Theory》1982,15(1):14-24
An elementary proof is given of the author's transformation formula for the Lambert series relating Gp(e2πiτ) to Gp(e2πiAτ), where p > 1 is an odd integer and is a general modular substitution. The method extends Sczech's argument for treating Dedekind's function , and uses Carlitz's formula expressing generalized Dedekind sums in terms of Eulerian functions. 相似文献
12.
Alan L.T Paterson 《Journal of Functional Analysis》1983,53(3):203-223
A theory of harmonic analysis on a metric group (G, d) is developed with the model of U, the unitary group of a C1-algebra , in mind. Essential in this development is the set of contractive, irreducible representations of G, and its concomitant set Pd(G) of positive-definite functions. It is shown that is compact and closed in . The set is determined in a number of cases, in particular when G = U() with abelian. If is an AW1-algebra, it is shown that d is essentially the same as . Unitary groups are characterised in terms of a certain Lie algebra u and several characterisations of G = U() when is abelian are given. 相似文献
13.
Joel M Cohen 《Journal of Functional Analysis》1982,48(3):301-309
Let G be a group and g1,…, gt a set of generators. There are approximately (2t ? 1)n reduced words in g1,…, gt, of length ?n. Let be the number of those which represent 1G. We show that exists. Clearly 1 ? γ ? 2t ? 1. is the cogrowth. 0 ? η ? 1. In fact . The entropic dimension of G is shown to be 1 ? η. It is then proved that d(G) = 1 if and only if G is free on g1,…, gt and d(G) = 0 if and only if G is amenable. 相似文献
14.
Tom Brylawski 《Discrete Mathematics》1977,18(3):243-252
In “The Slimmest Geometric Lattices” (Trans. Amer. Math. Soc.). Dowling and Wilson showed that if G is a combinatorial geometry of rank r(G) = n, and if X(G) = Σμ(0, x)λr ? r(x) = Σ (?1)r ? kWkλk is the characteristic polynomial of G, then Thus γ(G) ? 2r ? 1 (n+2), where γ(G) = Σwk. In this paper we sharpen these lower bounds for connected geometries: If G is connected, r(G) ? 3, and n(G) ? 2 ((r, n) ≠ (4,3)), then |μ| ? (r? 1)n; and γ ? (2r ? 1 ? 1)(2n + 2). These bounds are all achieved for the parallel connection of an r-point circuit and an (n + 1)point line. If G is any series-parallel network, , and then . Further, if β is the Crapo invariant, then β(G) ? max(1, n ? r + 2). This lower bound is achieved by the parallel connection of a line and a maximal size series-parallel network. 相似文献
15.
In this paper, we establish some relationships between the circuits of the connection-graph GC(F), and the circuits of theiteration-graph G1(F), of a monotone boolean function F. We first show that if G1(F) contains an element circuit of length multiple of p? {2,3}, then GC(F) contains an elementary circuit of length multiple of p; then we prove that if GC(F) is a subgraph of a caterpillar, then G1(F) is a subgraph of a tree; at last we exhibit an infinite family of monotone boolean functions {Fn; n = 2 × 5q, q ≥ 1} such that any GC(Fn) is a subgraph of a tree, and G1(Fn) contains a circuit of length 2q+1, i.e., of the order . 相似文献
16.
Let be a von Neumann algebra, let {αt}tεR be an ultraweakly continuous one-parameter group of 1-automorphisms of , and let be the set of all A such that for each ? in 1, the function t → ?(αt(A)) lies in H∞(. Then is an ultraweakly closed subalgebra of containing the identity which is proper and non-self-adjoint if {αt}tεR is not trivial. In this paper, a systematic investigation into the structure theory of is begun. Two of the more note-worthy developments are these. First of all, conditions under which is a subdiagonal algebra in , in the sense of Arveson, are determined. The analysis provides a common perspective from which to view a large number of hitherto unrelated algebras. Second, the invariant subspace structure of is determined and conditions under which is a reductive subalgebra of are found. These results are then used to produce examples where is a proper, non-self-adjoint, reductive subalgebra of . The examples do not answer the reductive algebra question, however, because although ultraweakly closed, the subalgebras are weakly dense in . 相似文献
17.
Let R = (r1,…, rm) and S = (s1,…, sn) be nonnegative integral vectors, and let (R, S) denote the class of all m × n matrices of 0's and 1's having row sum vector R and column sum vector S. An invariant position of (R, S) is a position whose entry is the same for all matrices in (R, S). The interchange graph G(R, S) is the graph where the vertices are the matrices in (R, S) and where two matrices are joined by an edge provided they differ by an interchange. We prove that when 1 ≤ ri ≤ n ? 1 (i = 1,…, m) and 1 ≤ sj ≤ m ? 1 (j = 1,…, n), G(R, S) is prime if and only if (R, S) has no invariant positions. 相似文献
18.
Lisa A Mantini 《Journal of Functional Analysis》1985,60(2):211-242
Starting from the realization of the Fock space as L2-cohomology of p + q, 0,p(p + q) = ⊕m?m0,p(p + q), an integral transform is constructed which is a direct-image mapping from m0,p(p + q) into the space of holomorphic sections of some vector bundle Em over M ≈ U(p, q)/(U(q) × U(p)), m ? 0. The transform intertwines the natural actions of U(p, q) and is injective if m ? 0, so it provides a geometric realization of the ladder representations of U(p, q). The sections in the image of the transform satisfy certain linear differential equations, which are explicitly described. For example, Maxwell's equations are of this form if p = q = 2 and m = 2. Thus, this transform is analogous to the Penrose correspondence. 相似文献
19.
P Frankl 《Journal of Combinatorial Theory, Series A》1977,22(2):249-251
The following conjecture of Katona is proved. Let X be a finite set of cardinality n, 1 ? m ? 2n. Then there is a family , || = m, such that F ∈ , G ? X, | G | > | F | implies G ∈ and minimizes the number of pairs (F1, F2), F1, F2 ∈ F1 ∩ F2 = ? over all families consisting of m subsets of X. 相似文献
20.
J.J.A.M Brands 《Journal of Mathematical Analysis and Applications》1978,63(1):54-64
This paper presents some comparison theorems on the oscillatory behavior of solutions of second-order functional differential equations. Here we state one of the main results in a simplified form: Let q, τ1, τ2 be nonnegative continuous functions on (0, ∞) such that τ1 ? τ2 is a bounded function on [1, ∞) and t ? τ1(t) → ∞ if t → ∞. Then is oscillatory if and only if is oscillatory. 相似文献