共查询到20条相似文献,搜索用时 281 毫秒
1.
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
2.
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
3.
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
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.
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
6.
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
7.
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
8.
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
9.
Let G be a connected amenable group (thus, an extension of a connected normal solvable subgroup R by a connected compact group ). We show how to explicitly construct sequences {Un} of compacta in G in terms of the structural features of G which have the following property: For any “reasonable” action G × Lp(X, μ) ↓ Lp(X, μ) on an Lp space, 1 <p < ∞, and any f ∈ Lp(X, μ), the averages converge in Lp norm, and pointwise μ-a.e. on X, to G-invariant functions in Lp(X, μ). A single sequence {Un} in G works for all Lp actions of G. This result applies to many nonunimodular groups, which are not handled by previous attempts to produce noncommutative generalizations of the pointwise ergodic theorem. 相似文献
10.
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
11.
Let x?Sn, the symmetric group on n symbols. Let θ? Aut(Sn) and let the automorphim order of x with respect to θ be defined by where xθ is the image of x under θ. Let αg? Aut(Sn) denote conjugation by the element g?Sn. Let where s and k are positive integers and denotes a divides b. Further h(s, k : n) ≡ b(1; s, k : n), where 1 denotes the identity automorphim. If g?Sn let c = f(g, s) denote the number of symbols in g which are in cycles of length not dividing the integer s, and let gs denote the product of all cycles in g whose lengths do not divide s. Then gs moves c symbols. The main results proved are: (1) recursion: if n ? c + 1 and t = n ? c ? 1 then (2) reduction: b(g; s, 1 : c)h(s, 1 : i) = b(g; s, 1 : i + c); (3) distribution: let D(θ, n) ≡ {(k, b) : k?Z+ and b = b(θ; 1, k : n) ≠ 0}; then D(θ, m) = D(φ, m) ∨ m ? N = N(θ, φ) iff θ is conjugate to φ; (4) evaluation: the number of cycles in gss of any given length is smaller than the smallest prime dividing s iff b(gs; s, 1 : c) = 1. If g = (12 … pm)t and then . 相似文献
12.
Michael Moses 《Annals of Pure and Applied Logic》1984,27(3):253-264
A successivity in a linear order is a pair of elements with no other elements between them. A recursive linear order with recursive successivities is recursively categorical if every recursive linear order with recursive successivities isomorphic to is in fact recursively isomorphic to . We characterize those recursive linear orders with recursive successivities that are recursively categorical as precisely those with order type k1+g1+k2+g2+…+gn-1+kn where each kn is a finite order type, non-empty for i?{2,…,n-1} and each gi is an order type from among {ω,ω*,ω+ω*}∪{k·η:k<ω}. 相似文献
13.
Let Tn, n = 1,2,… be a sequence of linear contractions on the space where is a finite measure space. Let M be the subspace of L1 for which Tng → g weakly in L1 for g?M. If Tn1 → 1 strongly, then Tnf → f strongly for all f in the closed vector sublattice in L1 generated by M.This result can be applied to the determination of Korovkin sets and shadows in L1. Given a set G ? L1, its shadow S(G) is the set of all f?L1 with the property that Tnf → f strongly for any sequence of contractions Tn, n = 1, 2,… which converges strongly to the identity on G; and G is said to be a Korovkin set if S(G) = L1. For instance, if 1 ?G, then, where M is the linear hull of G and M is the sub-σ-algebra of generated by {x?X: g(x) > 0} for g?M. If the measure algebra is separable, has Korovkin sets consisting of two elements. 相似文献
14.
Let G be a metric locally compact Abelian group. We prove that the spaces (L1, Lip(α, p)), (L1, lip(α, p)), Lip(α, p) and lip(α, p)~ are isometrically isomorphic, where Lip(α, p) and lip(α, p) denote the Lipschitz spaces defined on G, (L1, A) is the space of multipliers from L1 to A, and lip(α, p)~ denotes the relative completion of lip(α, p). We also show that . 相似文献
15.
Explicit and asymptotic solutions are presented to the recurrence M(1) = g(1), M(n + 1) = g(n + 1) + min1 ? t ? n(αM(t) + βM(n + 1 ? t)) for the cases (1) α + β < 1, is rational, and g(n) = δnI. (2) α + β > 1, min(α, β) > 1, is rational, and (a) g(n) = δn1, (b) g(n) = 1. The general form of this recurrence was studied extensively by Fredman and Knuth [J. Math. Anal. Appl.48 (1974), 534–559], who showed, without actually solving the recurrence, that in the above cases , where γ is defined by α?γ + β?γ = 1, and that does not exist. Using similar techniques, the recurrence M(1) = g(1), M(n + 1) = g(n + 1) + max1 ? t ? n(αM(t) + βM(n + 1 ? t)) is also investigated for the special case α = β < 1 and g(n) = 1 if n is odd = 0 if n is even. 相似文献
16.
In the first part of this Note, we show that the first non-zero eigenvalue of the Laplace operator on 1-forms of a standard congruence arithmetic complex hyperbolic n-manifold is always . The following parts of this Note concern homological applications of this result. We prove, in particular, that if Sh0H?Sh0G are two Shimura varieties of type U(n?1,1) and U(n,1), the natural map H2n?3(Sh0H)→H2n?3(Sh0G) is injective, first step of a “Lefschetz theorem” for Shimura varieties. To cite this article: N. Bergeron, L. Clozel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 995–998. 相似文献
17.
Misha Zafran 《Journal of Functional Analysis》1977,26(3):289-314
Let 1 < p < ∞ with p ≠ 2. Let G denote one of the groups n, n, or n. We show that only entire functions operate in certain algebras of multipliers on Lp(G). 相似文献
18.
Let g and n be positive integers and let . If θ(x) is a multiple of Σi = 0k ? 1xi, then the g-circulant whose Hall polynomial is equal to θ(x) satisfies the matrix equation in the title. If the g-circulant whose Hall polynomial is equal to Σi = 0h ? 1xi satisfies the matrix equation in the title, then h is a multiple of k. 相似文献
19.
Let A be an n × n matrix; write A = H+iK, where i2=—1 and H and K are Hermitian. Let f(x,y,z) = det(zI?xH?yK). We first show that a pair of matrices over an algebraically closed field, which satisfy quadratic polynomials, can be put into block, upper triangular form, with diagonal blocks of size 1×1 or 2×2, via a simultaneous similarity. This is used to prove that if , where g has degree 2, then for some unitary matrix U, the matrix U1AU is the direct sum of copies of a 2×2 matrix A1, where A1 is determined, up to unitary similarity, by the polynomial g(x,y,z). We use the connection between f(x,y,z) and the numerical range of A to investigate the case where f(x,y,z) has the form (z?αax? βy)r[g(x,y,z)]s, where g(x,y,z) is irreducible of degree 2. 相似文献
20.
Aleš Drápal 《Discrete Mathematics》1983,44(3):251-265
Let G be a group and a quasigroup on the same underlying set. Let dist() denote the number of pairs (x, y) ?G2 such that . For a finite quasigroup Q, n = card(Q), let t = dist(Q) = min dist(G, Q), where G runs through all groups with the same underlying set, and s = s(Q) the number of non-associative triples. Then 4tn?2t2?24t?s?4tn. If 1 ? s < 3n2/32, then 3tn < s holds as well. Let n ? 168 be an even integer and let σ = min s(Q), where Q runs through all non-associative quasigroups of order n. Then σ = 16n?64. 相似文献