共查询到20条相似文献,搜索用时 46 毫秒
1.
2.
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
3.
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
4.
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
5.
A , denoted by (λ; t, k, v), is a system of subsets of size k from a v-set X, such that each t-subset of X is contained in exactly λ elements of . A hypergraph is a finite set Y where is a family of subsets (which we assume here are distinct) of Y such that Ei≠Ø, i?l, and ?Ei=Y. Let G be an automorphism group of where Oli is the ith orbit of l-subsets of . Let A(G; H; t, k)= (aij) be an m by n matrix, where aij is the number of copies of Oti that occur in the system of all t-subsets of all elements of Okj. Then there is a t-design with , with parameters (λ; t, k, v), and with G an automorphism groupof T iff there is an m by s submatrix M of A(G; H; t, k) where M has uniform row sums λ. The calculus for applying this theorem is illustrated and numerous t-designs for 10?v?16 are found and presented. Using a theorem of Alltop on our (12; 4, 6, 13) and (60; 4, 7, 15) we obtain a (12; 5, 7, 14) and a (60; 5, 8, 16). 相似文献
6.
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
7.
We show that for a C1-dynamical system (A, G, α) with G discrete (abelian) the Connes spectrum Γ(α) is equal to if and only if every nonzero closed ideal in G × αA has a nonzero intersection with A. Denote by GJ the closed subgroup of G that leaves fixed the primitive ideal J of A. We show for a general group G that if all isotropy groups GJ are discrete, then GXαA is simple if and only if A is G-simple and . This result is applicable not only when G is discrete but also when G? or G? provided that A is not primitive. Specializing to single automorphisms (i.e., G=) we show that if (the transposed of) α acts freely on a dense set of points in , then Λ(α)=. The converse is only proved when A is of type I. 相似文献
8.
《Topology and its Applications》1987,25(2):203-223
If Λ is a ring and A is a Λ-module, then a terminal completion of Ext1Λ(A, ) is shown to exist if, and only if, ExtjΛ(A, P)=0 for all projective Λ-modules P and all sufficiently large j. Such a terminal completion exists for every A if, and only if, the supremum of the injective lengths of all projective Λ-modules, silp Λ, is finite. Analogous results hold for Ext1Λ(,A) and involve spli Λ, the supremum of the projective lengths of the injective Λ-modules. When Λ is an integral group ring G, spliG is finite implies silp G is finite. Also the finiteness of spli is preserved under group extensions. If G is a countable soluble group, the spli G is finite if, and only if, the Hirsch number of G is finite. 相似文献
9.
Frances Chevarley Edmonds 《Discrete Mathematics》1977,19(3):213-227
In this paper we studied m×n arrays with row sums and column sums where (n,m) denotes the greatest common divisor of m and n. We were able to show that the function Hm,n(r), which enumerates m×n arrays with row sums and column sums and respectively, is a polynomial in r of degree (m?1)(n?1). We found simple formulas to evaluate these polynomials for negative values, ?r, and we show that certain small negative integers are roots of these polynomials. When we considered the generating function Gm,n(y) = Σr?0Hm,n(r)yr, it was found to be rational of degree less than zero. The denominator of Gm,n(y) is of the form (1?y)(m?1)(n?1)+3, and the coefficients of the numerator are non-negative integers which enjoy a certain symmetric relation. 相似文献
10.
M.K Grammatikopoulos Y.G Sficas V.A Staikos 《Journal of Mathematical Analysis and Applications》1979,67(1):171-187
We regard a graph G as a set {1,…, v} together with a nonempty set E of two-element subsets of {1,…, v}. Let p = (p1,…, pv) be an element of nv representing v points in n and consider the realization G(p) of G in n consisting of the line segments [pi, pj] in n for {i, j} ?E. The figure G(p) is said to be rigid in n if every continuous path in nv, beginning at p and preserving the edge lengths of G(p), terminates at a point q ? nv which is the image (Tp1,…, Tpv) of p under an isometry T of n. We here study the rigidity and infinitesimal rigidity of graphs, surfaces, and more general structures. A graph theoretic method for determining the rigidity of graphs in 2 is discussed, followed by an examination of the rigidity of convex polyhedral surfaces in 3. 相似文献
11.
Hiroshi Takai 《Journal of Functional Analysis》1975,19(1):25-39
Let be a C1-algebra, and G be a locally compact abelian group. Suppose α is a continuous action of G on . Then there exists a continuous action ga of the dual group of G on the C1-crossed product by α such that the C1-crossed product is isomorphic to the tensor product and the C1-algebra of all compact operators on L2(G). 相似文献
12.
E.J Cockayne 《Journal of Combinatorial Theory, Series B》1974,17(2):183-187
The Ramsey Number r(G1, G2) is the least integer N such that for every graph G with N vertices, either G has the graph G1 as a subgraph or , the complement of G, has the graph G2 as a subgraph.In this paper we embed the paths Pm in a much larger class of trees and then show how some evaluations by T. D. Parsons of Ramsey numbers r(Pm, K1,n), where K1,n is the star of degree n, are also valid for r(Tm, K1,n) where Tm ∈ . 相似文献
13.
《Topology and its Applications》1986,22(2):109-122
We write 2x for the hyperspace of all non-empty compact sets in a complete metric linear space X topologized by the Hausdorff metric. Using the notation (X) = {A ϵ 2X: A is finite}, lf2 = {x} = (xi) ϵ l2: xi = 0 for almost all i}, and lσ2 = {x = (x i) ϵ l2:σ∞i=1 (ixi)2 < ∞}, we have the following theorem:A family ⊂(X) is homeomorphic to lf2 if is σ-fd-compact, the closure of in 2x is not locally compact and if whenever A, B ∈ , λ ∈ [0, 1] and C ⊂ λA + (1 - λ)B with card C⩽ max{card A, card B} then C ϵ .Moreover, for any Gδ-AR-set of with ⊃ we have (, )≅(l2, lƒ2).Similar conditions for hyperspaces to be homeomorphic to lσ2 are also established. 相似文献
14.
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
15.
J.F. Colombeau 《Journal of Mathematical Analysis and Applications》1983,94(1):96-115
If Ω denotes an open subset of n (n = 1, 2,…), we define an algebra (Ω) which contains the space ′(Ω) of all distributions on Ω and such that is a subalgebra of (Ω). The elements of (Ω) may be considered as “generalized functions” on Ω and they admit partial derivatives at any order that generalize exactly the derivation of distributions. The multiplication in (Ω) gives therefore a natural meaning to any product of distributions, and we explain how these results agree with remarks of Schwartz on difficulties concerning a multiplication of distributions. More generally if q = 1, 2,…, and —a classical Schwartz notation—for any G1,…,Gq∈G(σ), we define naturally an element . These results are applied to some differential equations and extended to the vector valued case, which allows the multiplication of vector valued distributions of physics. 相似文献
16.
Harrie Hendriks 《Journal of Pure and Applied Algebra》1978,10(3):227-232
Let G be a finitely generated accessible group. We will study the homology of G with coefficients in the left G-module H1(G;[G]). This G-module may be identified with the G-module of continuous functions with values in on the G-space of ends of G, quotiented by the constant functions. The main result is as follows: Suppose G is infinite, then the abelian group H1(G;H1(G;[G])) has rank 1 if G has a free subgroup of finite index and it has rank 0 if G has not. 相似文献
17.
The graph G(P) of a polyhedron P has a node corresponding to each vertex of P and two nodes are adjacent in G(P) if and only if the corresponding vertices of P are adjacent on P. We show that if P ? n is a polyhedron, all of whose vertices have (0–1)-valued coordinates, then (i) if G(P) is bipartite, the G(P) is a hypercube; (ii) if G(P) is nonbipartite, then G(P) is hamilton connected. It is shown that if P ? n has (0–1)-valued vertices and is of dimension d (≤n) then there exists a polyhedron P′ ? d having (0–1)-valued vertices such that . Some combinatorial consequences of these results are also discussed. 相似文献
18.
Let H be a complex Hilbert space, P+ an orthogonal projection on H, and P? the complementary projection. If is any symmetrically normed ideal in the ring of bounded operators on H, then we consider the group of unitary operators on H such that P+UP?and P?UP+ lie in . When is the Hilbert-Schmidt class, these unitaries define automorphisms of the C1-algebra of the canonical anticommutation relations over H which are implementable in the representation of determined by P?. We investigate the structure of the group , proving in particular that it has infinitely many connected components, k, labelled by the Fredholm index of P+UP+. The connected component of the identity, 0, is generated by unitaries of the form exp(iA), with A self-adjoint and P+AP? in . Finally we consider an application of these results to two dimensional field theory, showing in particular that the charge and chiral charge quantum numbers arise as the Fredholm indices of P±UP± for certain unitary U on L2(, 2) 相似文献
19.
W. Cary Huffman 《Discrete Mathematics》1979,26(2):129-143
Let C be a binary code of length n and let JC (a, b, c, d) be its biweight enumerator. If n is even and C is self-dual, then JC is an element of the ring R of absolute invariants of a certain group . Under the additional assumption that all codewords of C have weight divisible by 4, a similar result holds with a different group. If n is odd and C is maximal self-orthogonal, then JC is an element of a certain R-module. Again a similar result holds if the codewords of C have weights divisible by 4. The groups involved are related to finite groups generated by reflections. In this paper the structure of these groups is described, and polynomial bases for the rings and modules in question are obtained. This answers a question posed in The Theory of Error- correcting Codes by F.J. MacWilliams and N.J.A. Sloane. 相似文献
20.
R.Grant Woods 《Topology and its Applications》1985,21(3):287-295
Let be a closed-hereditary topological property preserved by products. Call a space -regular if it is homeomorphic to a subspace of a product of spaces with . Suppose that each -regular space possesses a -regular compactification. It is well-known that each -regular space X is densely embedded in a unique space γscPX with such that if f: X → Y is continuous and Y has , then f extends continuously to γscPX. Call -pseudocompact if γscPX is compact.Associated with is another topological property #, possessing all the properties hypothesized for above, defined as follows: a -regular space X has # if each -pseudocompact closed subspace of X is compact. It is known that the -pseudocompact spaces coincide with the #-pseudocompact spaces, and that # is the largest closed-hereditary, productive property for which this is the case. In this paper we prove that if is not the property of being compact and -regular, then # is not simply generated; in other words, there does not exist a space E such that the spaces with # are precisely those spaces homeomorphic to closed subspaces of powers of E. 相似文献