共查询到20条相似文献,搜索用时 62 毫秒
1.
H. Samea 《Mathematica Slovaca》2014,64(4):871-878
In this paper, some relations between L p -spaces on locally compact groups are found. Applying these results proves that for a locally compact group G, the convolution Banach algebras L p (G) ∩ L 1(G) (1 < p ≤ ∞), and A p (G) ∩ L 1(G) (1 < p < ∞) are amenable if and only if G is discrete and amenable. 相似文献
2.
Let R(Γ, G) be the variety of representations of a finitely generated group Γ in a simple complex algebraic group G. We establish some sufficient conditions for the image of the diagonal representation ϱ = (ϱ1, …, ϱt), ϱi ε R(Γ, G), to be dense in Gf in the complex topology (“weak approximation”). 相似文献
3.
Ali Ghaffari 《Czechoslovak Mathematical Journal》2012,62(3):729-742
Let G be a locally compact group. We continue our work [A. Ghaffari: Γ-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of Γ-amenability of a locally compact group G defined with respect to a closed subgroup Γ of G × G. In this paper, among other things, we introduce and study a closed subspace A Γ p (G) of L ∞(Γ) and then characterize the Γ-amenability of G using A Γ p (G). Various necessary and sufficient conditions are found for a locally compact group to possess a Γ-invariant mean. 相似文献
4.
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
5.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(12):1333-1338
Let G be the group of real points of a reductive algebraic ℚ-group satisfying the same assumptions as in [5], Chapter I, and let Γ be a discrete subgroup of G. Let RΓ be the right regular representation of G in L2(Γ\G). We prove in this Note that, for any integrable rapidly decreasing function ƒ on G, the restriction of RΓ(ƒ) to the discrete spectrum of RΓ is a trace class operator. 相似文献
6.
《Journal of Combinatorial Theory, Series B》1986,41(3):255-274
Let Γ be a graph and G ≤ Aut(Γ). The group G is said to act distance-transitively on Γ if, for any vertices x, y, u, v such that ∂(x, y) = ∂(u, v), there is an element g ϵ G mapping x into u and y into v. If G acts distance-transitively on Γ then the permutation group induced by the action of G on the vertex set of Γ is called the distance-transitive representation of G. In the paper all distance-transitive representations of the symmetric groups Sn are classified. Moreover, all pairs (G, Γ) such that G acts distance-transitively on Γ and G = Sn for some n are described. The classification problem for these pairs was posed by N. Biggs (Ann. N.Y. Acad. Sci. 319 (1979), 71–81). The problem is closely related to the general question about distance-transitive graphs with given automorphism group. 相似文献
7.
Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k - 2)-Gorenstein with the injective dimensions of Λ U and U Γ being k, then the socle of the last term in a minimal injective resolution of Λ U is non-zero. 相似文献
8.
Let denote the real line and L∞(R), the class of all Borel measurable L∞-functions of . Let S ≠ {0} or φ, be a linear subspace of L∞(R) which is (i) translation invariant, (ii) weak1-closed, (iii) self-adjoint, i.e., f?S implies f?S, and (iv) an algebra. Then either (a) S = all constant functions in L∞; or (b) S = L∞; or (c) there is a unique c > 0 such that S consists of all L∞-functions which are periodic of period c.Extension of the above characterization of periodic subalgebras of L∞ to LCA groups are presented. Also it is shown that the above characterization is in various ways best possible. 相似文献
9.
Let Γ be a finite connected G-vertex-transitive graph and let v be a vertex of Γ. If the permutation group induced by the action of the vertex-stabiliser G v on the neighbourhood Γ(v) is permutation isomorphic to L, then (Γ,G) is said to be locally L. A permutation group L is graph-restrictive if there exists a constant c(L) such that, for every locally L pair (Γ,G) and a vertex v of Γ, the inequality |G v |≤c(L) holds. We show that an intransitive group is graph-restrictive if and only if it is semiregular. 相似文献
10.
Given a group automorphism ?: Γ?→?Γ, one has an action of Γ on itself by ?-twisted conjugacy, namely, g.x?=?gx?(g ?1). The orbits of this action are called ?-conjugacy classes. One says that Γ has the R∞-property if there are infinitely many ?-conjugacy classes for every automorphism ? of Γ. In this paper we show that any irreducible lattice in a connected semisimple Lie group having finite centre and rank at least 2 has the R∞-property. 相似文献
11.
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
12.
V. I. Zenkov 《Siberian Mathematical Journal》2018,59(2):264-269
Given a finite group G with socle isomorphic to L n (2 m ), we describe (up to conjugacy) all ordered pairs of primary subgroups A and B in G such that A ∩ B g ≠ 1 for all g ∈ g. 相似文献
13.
V. I. Zenkov 《Siberian Mathematical Journal》2016,57(6):1002-1010
Given a finite group G with socle isomorphic to L 2(q), q ≥ 4, we describe, up to conjugacy, all pairs of nilpotent subgroups A and B of G such that A ∩ B g ≠ 1 for all g ∈ G. 相似文献
14.
J. Extremera 《Journal of Functional Analysis》2003,197(1):212-227
Let G be a compact group. If the trivial representation of G is not weakly contained in the left regular representation of G on L02(G) and X is either Lp(G) for 1<p?∞ or C(G), then we show that every complete norm |·| on X that makes translations from (X,|·|) into itself continuous is equivalent to ||·||p or ||·||∞ respectively. If 1<p?∞ and every left invariant linear functional on Lp(G) is a constant multiple of the Haar integral, then we show that every complete norm |·| on Lp(G) that makes translations from (Lp(G),|·|) into itself continuous and that makes the map t?Lt from G into bounded is equivalent to ||·||p. 相似文献
15.
Chan-nan Chang 《Journal of Algebra》1974,30(1-3)
Let L be a lattice over the integers of a local field F which has a nontrivial involution. Then U+(L) (the subgroup of rotations of the unitary group U(L)) is generated by unitary transvections and quasitransvections contained in U+(L) (Theorem 7.8). Let g be a tableau. Then the mixed commutator subgroup of U+(L) and U(g) (the congruence subgroup of U+(L) corresponding to g) equals E(g) (the subgroup generated by unitary transvections and quasitransvections with orders contained in g) (Theorem 7.7). Finally, let G be a subgroup of U+(L) with o(G) = g, then G is a normal subgroup of U+(L) if and only if U(g) G E(g). 相似文献
16.
Wang Guojun 《Journal of Mathematical Analysis and Applications》1983,94(1):1-23
Let (Ω, , μ) be a probability space and let be a subsigma algebra of . Let A= L∞Ω, , μ , let A= L∞Ω, , μ, and let f?A. It is shown that best L∞-approximations of f by elements of B comprise an interval in B; that is, there exists such that a function g?B is a best L∞-approximation to f if and only if a.e. on Ω. The difference, , of and f is completely characterized in terms of special sets that have been developed in [2]. Then it is established that the best best L∞-approximation, f,∞, to f by elements of B is the average of and , where the function f,∞ is defined by f,∞(ω) limp → ∞f,P(ξ) and f,P denotes the best Lp-approximation to f elements of Lp(Ω, , μ). 相似文献
17.
We consider Gammaoperators G n on suitable Sobolev type subspaces of L p(0, ∞) and characterize the global rate of approximation of derivatives f (r) through corresponding derivatives (G n f)(r) in an appropriate weighted L p — metric by the rate of Ditzian and Totik’s second order weighted modulus of smoothness. 相似文献
18.
19.
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
20.
Mordechay B. Levin 《Israel Journal of Mathematics》2010,178(1):61-106
In this paper we describe a third class of low discrepancy sequences. Using a lattice Γ ? ? s , we construct Kronecker-like and van der Corput-like ergodic transformations T 1,Γ and T 2,Γ of [0, 1) s . We prove that for admissible lattices Γ, (T ν,Γ n (x))n≥0 is a low discrepancy sequence for all x ∈ [0, 1) s and ν ∈ {1, 2}. We also prove that for an arbitrary polyhedron P ? [0, 1) s , for almost all lattices Γ ∈ L s = SL(s,?)/SL(s, ?) (in the sense of the invariant measure on L s ), the following asymptotic formula holds with arbitrary small ? > 0, for all x ∈ [0, 1) s , and ν ∈ {1, 2}.
相似文献
$\# \{ 0 \le n < N:T_{v,\Gamma }^n(x) \in P\} = NvolP + O({(\ln N)^{s + \varepsilon }}),N \to \infty$