On spaces of p-adic vector measures

LetX be a Hausdorff zero-dimensional topological space,K(X) the algebra of all clopen subsets of X, E a Hausdorff locally convex space over a non-Archimedean valued field and C _b (X) the space of all bounded continuous -valued functions on X. The space M(K(X),E), of all bounded finitely-additive measures m: K(X) → E, is investigated. If we equip C _b (X) with the topologies β _o , β, β _u , τ _b or β _ob , it is shown that, for E (compete, the corresponding spaces of continuous linear operators from C _b (X) to E (are algebraically isomorphic to certain subspaces of M(K(X),E). The text was submitted by the author in English.     

Positive vector measures with given marginals

Suppose E is an ordered locally convex space, X ₁ and X ₂ Hausdorff completely regular spaces and Q a uniformly bounded, convex and closed subset of M _t ⁺ (X ₁ × X ₂, E). For i = 1, 2, let μ _i   M _t ⁺ (X _i , E). Then, under some topological and order conditions on E, necessary and sufficient conditions are established for the existence of an element in Q, having marginals μ ₁ and μ ₂.     

Strict Topologies as Topological Algebras

Let X be a completely regular Hausdorff space, C_b(X) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m-convex.     

Weighted composition operators on nonlocally convex weighted spaces of continuous functions

LetV be a system of weights on a completely regular Hausdorff spaceX and letB(E) be the topological vector space of all continuous linear operators on a general topological vector spaceE. LetCV ₀(X, E) andCV _b (X, E) be the weighted spaces of vector-valued continuous functions (vanishing at infinity or bounded, respectively) which are not necessarily locally convex. In the present paper, we characterize in this general setting the weighted composition operatorsW _π,? onCV ₀(X, E) (orCV _b (X, E)) induced by the operator-valued mappings π:X→B(E) (or the vector-valued mappings π:X→E, whereE is a topological algebra) and the self-map ? ofX. Also, we characterize the mappings π:X→B(E) (or π:x→E) and ?:X→X which induce the compact weighted composition operators on these weighted spaces of continuous functions.     

An identity on the maximum of a set of random variables

It is shown that if X₁, X₂, …, X_n are symmetric random variables and max(X₁, …, X_n)⁺ = max(0, X₁, …, X_n), then E[max(X₁,…,X_n)⁺]=[max(X₁,X₁,+X₂,+X₁,+X₃,…X₁,+X_n)⁺], and in the case of independent identically distributed symmetric random variables, E[max(X₁, X₂)⁺] = E[(X₁)⁺] + (1/2)E[(X₁ + X₂)⁺], so that for independent standard normal random variables, E[max(X₁, X₂)⁺] = (1/√2π)[1 + (1/√2)].     

A Construction Method for Albert Algebras over Algebraic Varieties

We construct cubic Jordan algebras over an integral proper scheme X such that 2, 3 ∈ H ⁰(X, 𝒪 _X ), generalizing a construction by B. N. Allison and J. R. Faulkner. In the process, we obtain admissible cubic algebras and pseudocomposition algebras over X. Results on the structure of these algebras are obtained, as well as examples over elliptic curves.     

A geometrical analysis of the efficient outcome set in multiple objective convex programs with linear criterion functions

This article performs a geometrical analysis of the efficient outcome setY _E of a multiple objective convex program (MLC) with linear criterion functions. The analysis elucidates the facial structure ofY _E and of its pre-image, the efficient decision setX _E . The results show thatY _E often has a significantly-simpler structure thanX _E . For instance, although both sets are generally nonconvex and their maximal efficient faces are always in one-to-one correspondence, large numbers of extreme points and faces inX _E can map into non-facial subsets of faces inY _E , but not vice versa. Simple tests for the efficiency of faces in the decision and outcome sets are derived, and certain types of faces in the decision set are studied that are immune to a common phenomenon called collapsing. The results seem to indicate that significant computational benefits may potentially be derived if algorithms for problem (MLC) were to work directly with the outcome set of the problem to find points and faces ofY _E , rather than with the decision set.     

On the local minimaxity of a test of independence in incomplete samples

Summary LetX=(X ₁,X ₂) be ap-dimensional normal variable. Suppose that we haven independent observations onX andm, independent observations onX _i ,i=1,2, respectively. For testing the independence betweenX ₁ andX ₂, Eaton and Kariya (1983),Ann. Statist.,11, 654–665) obtains a locally most powerful test among the class of tests invariant under the group of affine transformations. In this paper, this LMPI test is shown to be locally minimax within the class of all tests of the same level.     

Locally Compact Path Spaces

It is shown that the space X^[0,1], of continuous maps [0,1]X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T₁-space X, it follows that X^[0,1] is locally compact if and only if X is locally compact and totally path-disconnected. Mathematics Subject Classifications (2000) 54C35, 54E45, 55P35, 18B30, 18D15.     

Product of uniform measures

For i =  (1, 2), let X _i be Hausdorff uniform spaces and μ _i uniform measures on X _i . We determine the existence of the product uniform measure μ ₁⊗μ ₂ on X ₁  ×  X ₂ and prove a Fubini type theorem and a continuity property. The result is extended to vector-valued uniform measures.      

Non-conflicting ordering cones and vector optimization in inductive limits

Let (E, ξ)= ind (E_n, ξ_n) be an inductive limit of a sequence (E_n, ξ_n)_{n∈ N} of locally convex spaces and let every step (E_n, ξ_n) be endowed with a partial order by a pointed convex (solid) cone S_n. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence (S_n)_{n∈ N} of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.     

相关序的进一步研究

Let (X1,X2,…,Xn) and (Y1,Y2,…Yn) be real random vectors with the same marginal distributions,if (X1,X2,…,Xn)≤c(Y1,Y2,…Yn), it is showed in this paper that ∑i=1^n Xi≤cx∑i=1^n Yi and max1≤k≤n∑i=1^k Xi≤icx max1≤k≤n∑i=1^k Yi hold. Based on this fact,a more general comparison theorem is obtained.     

Spaces of Densely Continuous Forms, USCO and Minimal USCO Maps

Our paper studies the topology of uniform convergence on compact sets on the space of densely continuous forms (introduced by Hammer and McCoy (1997)), usco and minimal usco maps. We generalize and complete results from Hammer and McCoy (1997) concerning the space D(X,Y) of densely continuous forms from X to Y. Let X be a Hausdorff topological space, (Y,d) be a metric space and D _k (X,Y) the topology of uniform convergence on compact sets on D(X,Y). We prove the following main results: D _k (X,Y) is metrizable iff D _k (X,Y) is first countable iff X is hemicompact. This result gives also a positive answer to question 4.1 of McCoy (1998). If moreover X is a locally compact hemicompact space and (Y,d) is a locally compact complete metric space, then D _k (X,Y) is completely metrizable, thus improving a result from McCoy (1998). We study also the question, suggested by Hammer and McCoy (1998), when two compatible metrics on Y generate the same topologies of uniform convergence on compact sets on D(X,Y). The completeness of the topology of uniform convergence on compact sets on the space of set-valued maps with closed graphs, usco and minimal usco maps is also discussed.     

A full-invariant theorem and some applications

Let (X,τ₁) and (Y,τ₂) be two Hausdorff locally convex spaces with continuous duals X′ and Y′, respectively, L(X,Y) be the space of all continuous linear operators from X into Y, K(X,Y) be the space of all compact operators of L(X,Y). Let WOT and UOT be the weak operator topology and uniform operator topology on K(X,Y), respectively. In this paper, we characterize a full-invariant property of K(X,Y); that is, if the sequence space λ has the signed-weak gliding hump property, then each λ-multiplier WOT-convergent series ∑_iT_i in K(X,Y) must be λ-multiplier convergent with respect to all topologies between WOT and UOT if and only if each continuous linear operator T :(X,τ₁)→(λ^β,σ(λ^β,λ)) is compact. It follows from this result that the converse of Kalton's Orlicz–Pettis theorem is also true.     

Computing the nearest stable matrix pairs

In this paper, we study the nearest stable matrix pair problem: given a square matrix pair (E,A), minimize the Frobenius norm of (Δ_E,Δ_A) such that (E+Δ_E,A+Δ_A) is a stable matrix pair. We propose a reformulation of the problem with a simpler feasible set by introducing dissipative Hamiltonian matrix pairs: A matrix pair (E,A) is dissipative Hamiltonian if A=(J−R)Q with skew‐symmetric J, positive semidefinite R, and an invertible Q such that Q^TE is positive semidefinite. This reformulation has a convex feasible domain onto which it is easy to project. This allows us to employ a fast gradient method to obtain a nearby stable approximation of a given matrix pair.     

The strong approximation of extremal processes

Summary If X ₁, X ₂, ..., are i.i.d. random variables and Y _n =Max(X ₁, ..., X _n ); if for some sequences A _n , B_n, n=1, 2, ..., E _n (t)=A_nY_[nt]+B_n is such that E _n (1) weakly converges to a non degenerate limit distribution, then we prove that it is possible to construct a sequence of replicates of extremal processes E ⁽ⁿ⁾(t) on the same probability space, such that d(E _n (.), E ⁽ⁿ⁾(.))0 a.s., with the Levy metric. We give the rates of consistency of the approximations.     

Barrelledness of Spaces with Toeplitz Decompositions

A Toeplitz decomposition of a locally convex space E into subspaces (E_k) with projections (P_k) is a decomposition of every x  E as x = ∑_kP_kx, where ordinary summability has been replaced by summability with respect to an infinite and lower triangular regular matrix. We extend to the setting of Toeplitz decompositions a couple of results about barrelledness of Schauder decompositions. The first result, given for Schauder decompositions by Noll and Stadler, links the barrelledness of a normed space E to the barrelledness of the pieces E_k via the fact that E′ is big enough so as to coincide with its summability dual. Our second theorem, given for Schauder decompositions by Dı́az and Miñarro, links the quasibarrelledness of an ₀-quasibarrelled (in particular, (DF)) space E to the quasibarrelledness of the pieces E_k via the fact that the decomposition is simple.     

On almost sure convergence of amarts and martingales without the Radon-Nikodym property

It is shown here that for any Banach spaceE-valued amart (X _n) of classB, almost sure convergence off(X_n) tof(X) for eachf in a total subset ofE ^* implies scalar convergence toX.     

More results on perfect (3,3,6k + 4; 6k − 2)‐threshold schemes

A (2,3)‐packing on X is a pair (X, ), where is a set of 3‐subsets (called blocks) of X, such that any pair of distinct points from X occurs together in at most one block. Its leave is a graph (X,E) such that E consists of all the pairs which do not appear in any block of . In this article, we shall construct a set of 6k ? 2 disjoint (2,3)‐packings of order 6k + 4 with K_1,3 ∪ 3kK₂ or G₁ ∪ (3k ? 1)K₂ as their common leave for any integer k ≥ 1 with a few possible exceptions (G₁ is a special graph of order 6). Such a system can be used to construct perfect threshold schemes as noted by Schellenberg and Stinson ( 22 ). © 2006 Wiley Periodicals, Inc. J Combin Designs     

Counterexample to Peano's theorem in infinite-dimensionalF′-spaces

LetE be a nonnormable Fréchet space, and letE′ be the space of all continuous linear functionals onE in the strong topology. A continuous mappingf:E′→E′ such that for anyt ₀∈ℝ,x ₀∈E′, the Cauchy problemx=f(x), x(t ₀ )=x ₀ has no solutions is constructed. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 128–137, July, 1997. Translated by V. N. Dubrovsky