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1.
LetX be any compact convex subset of a locally convex Hausdorff space andE be a complex Banach space. We denote byA(X, E) the space of all continuous and affineE-valued functions defined onX. In this paper we prove thatX is a Choquet simplex if and only if the dual ofA(X, E) is isometrically isomorphic by a selection map toM m (X, E*), the space ofE*-valued,w*-regular boundary measures onX. This extends and strengthens a result of G. M. Ustinov. To do this we show that for any compact convex setX, each element of the dual ofA(X, E) can be represented by a measure inM m (X, E*) with the same norm, and this representation is unique if and only ifX is a Choquet simplex. We also prove that ifX is metrizable andE is separable then there exists a selection map from the unit ball of the dual ofA(X, E) into the unit ball ofM m (X, E*) which is weak* to weak*-Borel measurable.This work will constitute a portion of the author's Ph.D. Thesis at the University of Illinois.  相似文献   

2.
In this paper we study the spaces ∞p(E, X) of p-lattice summing operators from a Banach space E to a Banach lattice X. The main results characterize those E and X for which Δp(E, X) = IIp(E, X) and we show that ∞(E, X)=Δ2(E, X) for an infinite dimensional Banach lattice X of finite cotype if and only if E is isomorphic to a Hilbert space.  相似文献   

3.
On the supercyclicity and hypercyclicity of the operator algebra   总被引:1,自引:0,他引:1  
Let B(X) be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or *-strong topology. We give sufficient conditions for a continuous linear mapping L : B(X) →B(X) to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied' by Chan and here we obtain an analogous result in the case of *-strong operator topology.  相似文献   

4.
The rotation flow on the circle T gives a concrete representation of the irrational rotation algebra, which is an in finite dimensional simple quotient of the group C*‐algebra of the discrete Heisenberg group H3 analogously certain 2‐ and 3‐dimensional Anzai flows on T 2 and T 3are known to give concrete representations of the corresponding quotients of the group C*‐algebras of the groups H4 and H5,5. Considered here is the (minimal, effective) 4‐dimensional Anzai flow F = (ℤ, T 4) generated by the homeomorphism (y, x, w, v) ↦ (λy, yx, xw, wv); a group H6,10 is determined by F the faithful in finite dimensional simple quotients of whose group C*‐algebra C*‐(H6,10 have concrete representations given by F. Furthermore, the rest of the infinite dimensional simple quotients of C*‐(H6,10 are identified and displayed as C*‐crossed products generated by minimal effective actions and also as matrix algebras over simple C*‐algebras from groups of lower dimension; these lower dimensional groups are H3 and subgroups of H4 and H5,5.  相似文献   

5.
Given a simple plane graph G, an edge‐face k‐coloring of G is a function ? : E(G) ∪ F(G) → {1,…,k} such that, for any two adjacent or incident elements a, bE(G) ∪ F(G), ?(a) ≠ ?(b). Let χe(G), χef(G), and Δ(G) denote the edge chromatic number, the edge‐face chromatic number, and the maximum degree of G, respectively. In this paper, we prove that χef(G) = χe(G) = Δ(G) for any 2‐connected simple plane graph G with Δ (G) ≥ 24. © 2005 Wiley Periodicals, Inc. J Graph Theory  相似文献   

6.
The following results are proved in this paper. Let G be a 2k-edge-connected eulerian graph. (i) For every set {e1, e2, ?, e2k+1} ? E(G) there is an eulerian trail T of the form e1, e2, ?, e2k+1, ?. (ii) For every set E* = {e1, e2, ?, ek} ? E(G) there is an eulerian trail T = e1, ?, e2, ?, ek, ? in which the elements of E* are traversed in accordance with a prescribed orientation. © 1995 John Wiley & Sons, Inc.  相似文献   

7.
UniversalC*-algebrasC*(A) exist for certain topological *-algebras called algebras with aC*-enveloping algebra. A Frechet *-algebraA has aC*-enveloping algebra if and only if every operator representation ofA mapsA into bounded operators. This is proved by showing that every unbounded operator representation π, continuous in the uniform topology, of a topological *-algebraA, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through the enveloping pro-C*-algebraE(A) ofA. Given aC*-dynamical system (G,A,α), any topological *-algebraB containingC c (G,A) as a dense *-subalgebra and contained in the crossed productC*-algebraC*(G,A,α) satisfiesE(B) =C*(G,A,α). IfG = ℝ, ifB is an α-invariant dense Frechet *-subalgebra ofA such thatE(B) =A, and if the action α onB ism-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS(ℝ,B,α) satisfiesE(S(ℝ,B,α)) =C*(ℝ,A,α). WhenG is a Lie group, theC -elementsC (A), the analytic elementsC ω(A) as well as the entire analytic elementsC є(A) carry natural topologies making them algebras with aC*-enveloping algebra. Given a non-unitalC*-algebraA, an inductive system of idealsI α is constructed satisfyingA =C*-ind limI α; and the locally convex inductive limit ind limI α is anm-convex algebra with theC*-enveloping algebraA and containing the Pedersen idealK a ofA. Given generatorsG with weakly Banach admissible relationsR, we construct universal topological *-algebraA(G, R) and show that it has aC*-enveloping algebra if and only if (G, R) isC*-admissible.  相似文献   

8.
A graph G = (V, E) is called (k, k′)‐total weight choosable if the following holds: For any total list assignment L which assigns to each vertex x a set L(x) of k real numbers, and assigns to each edge e a set L(e) of k′ real numbers, there is a mapping f: VE→? such that f(y)∈L(y) for any yVEand for any two adjacent vertices x, x′, . We conjecture that every graph is (2, 2)‐total weight choosable and every graph without isolated edges is (1, 3)‐total weight choosable. It follows from results in [7] that complete graphs, complete bipartite graphs, trees other than K2 are (1, 3)‐total weight choosable. Also a graph G obtained from an arbitrary graph H by subdividing each edge with at least three vertices is (1, 3)‐total weight choosable. This article proves that complete graphs, trees, generalized theta graphs are (2, 2)‐total weight choosable. We also prove that for any graph H, a graph G obtained from H by subdividing each edge with at least two vertices is (2, 2)‐total weight choosable as well as (1, 3)‐total weight choosable. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:198‐212, 2011  相似文献   

9.
A vertex labeling f : V → Z2 of a simple graph G = (V, E) induces two edge labelings f+ , f*: E → Z2 defined by f+ (uv) = f(u)+f(v) and f*(uv) = f(u)f(v). For each i∈Z2 , let vf(i) = |{v ∈ V : f(v) = i}|, e+f(i) = |{e ∈ E : f+(e) = i}| and e*f(i)=|{e∈E:f*(e)=i}|. We call f friendly if |vf(0)-vf(1)|≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets{|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)| : f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.  相似文献   

10.
It is shown that every proper weak* closed face of the closed unit ball E1*{E_1^*} in the dual space of a JB*-triple E coincides with set of all elements in the unit sphere of E* attaining their norm at a unique compact tripotent in E**. In particular every proper weak* closed face of the closed unit ball E1*{E_1^*} is weak*-semi-exposed. This result provides an affirmative answer to a conjecture posed over 20 years ago.  相似文献   

11.
Given a graph H and a positive integer n, Anti‐Ramsey number AR(n, H) is the maximum number of colors in an edge‐coloring of Kn that contains no polychromatic copy of H. The anti‐Ramsey numbers were introduced in the 1970s by Erd?s, Simonovits, and Sós, who among other things, determined this function for cliques. In general, few exact values of AR(n, H) are known. Let us call a graph H doubly edge‐critical if χ(H?e)≥p+ 1 for each edge eE(H) and there exist two edges e1, e2 of H for which χ(H?e1?e2)=p. Here, we obtain the exact value of AR(n, H) for any doubly edge‐critical H when n?n0(H) is sufficiently large. A main ingredient of our proof is the stability theorem of Erd?s and Simonovits for the Turán problem. © 2009 Wiley Periodicals, Inc. J Graph Theory 61: 210–218, 2009  相似文献   

12.
We study weak limits of the extreme points, ∂ e (E * 1), of the dual ball of a JB*-triple, E. We show that all such weak limits, except possibly the zero functional, are weak sequential limits and we discuss implications for the structure of E. Received: 9 April 2001  相似文献   

13.
In this note we show that the bilocal *-automorphisms of the C*-algebra B(H) of all bounded linear operators acting on a complex infinite dimensional separable Hilbert space H are precisely the unital algebra *-endomorphisms of B(H).  相似文献   

14.
If T or T* is an algebraically quasi-class A operator acting on an infinite dimensional separable Hilbert space then we prove that Weyl’s theorem holds for f(T) for every f H(σ(T)), where H(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is algebraically quasi-class A then a-Weyl’s theorem holds for f(T). Also, if T or T* is an algebraically quasi-class A operator then we establish that the spectral mapping theorems for the Weyl spectrum and the essential approximate point spectrum of T for every f H(σ(T)), respectively. This research was supported by the Kyung Hee University Research Fund in 2007 (KHU- 20071605).  相似文献   

15.
16.
A group G is said to be in Ek*E_k^* (k a positive integer), if every infinite subset of G contains a pair of elements that generate a k-Engel group.¶It is shown that a finitely generated locally graded group G in Ek*E_k^* is a finite-by- (k-Engel) group, in particular a finite extension of a k-Engel group.  相似文献   

17.
This paper considers the isometric extension problem concerning the mapping from the unit sphere S 1(E) of the normed space E into the unit sphere S 1(l (Γ)). We find a condition under which an isometry from S 1(E) into S 1(l (Γ)) can be linearly and isometrically extended to the whole space. Since l (Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are solved. More precisely, if E and F are two normed spaces, and if V 0: S 1(E) → S 1(F) is a surjective isometry, where c 00(Γ) ⊆ Fl (Γ), then V 0 can be extended to be an isometric operator defined on the whole space. This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614)  相似文献   

18.
Nuclear convergence spaces are studied. It is shown that an Le-embedded convergence vector space E is LeLM-embedded if it is Schwartz and satisfies a certain countability condition which expresses that the set of filters converging to zero is essentially countable. Further it is shown that if E is LeLM-embedded and nuclear, then the identity EE can be approximated with finite operators in the equable continuous convergence structure on L(E, E). This result is used in the study of the spectrum HomcHe(U) of the convergence algebra He(U) of holomorphic functions on a circled convex open set to prove sufficient conditions for the validity of the formula HomcHe(U) ~ U.  相似文献   

19.
We introduce a geometrical property of norm one complemented subspaces ofC(K) spaces which is useful for computing lower bounds on the norms of projections onto subspaces ofC(K) spaces. Loosely speaking, in the dual of such a space ifx* is a w* limit of a net (x a * ) andx*=x*1+x*2 with ‖x*‖=‖x*1‖ + ‖x*2‖, then we measure how efficiently thex a * 's can be split into two nets converging tox*1 andx*2, respectively. As applications of this idea we prove that if for everyε>0,X is a norm (1+ε) complemented subspace of aC(K) space, then it is norm one complemented in someC(K) space, and we give a simpler proof that a slight modification of anl 1-predual constructed by Benyamini and Lindenstrauss is not complemented in anyC(K) space. Research partially supported by a grant of the U.S.-Israel Binational Science Foundation. Research of the first-named author is supported in part by NSF grant DMS-8602395. Research of the second-named author was partially supported by the Fund for the Promotion of Research at the Technion, and by the Technion VPR-New York Metropolitan Research Fund.  相似文献   

20.
We show that a manifold-stratified space X is the interior of a compact manifold-stratified space with boundary if and only if X is tame-ended and a K-theoretic obstruction γ*(X) vanishes. The obstruction γ*(X) is a localization of Quinn's mapping cylinder neighborhood obstruction. The main results are Theorem 1.6 and Theorem 1.7 below. In particular, this explains when a G-manifold is the interior of a compact G-manifold with boundary. One of our methods is a new transversality theorem, Theorem 1.16. Oblatum 30-VI-1996 & 21-X-1997 / Published online: 14 January 1999  相似文献   

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