In this paper we study the Pareto efficiency with respect to a locally nuclear cone in the product of two locally convex spaces with the restricted assumption that only some related sets are locally complete.

View full abstract

We discuss the idea of peripheral spectrum and related concepts such as Maximum modulus set, peak sets etc. for a function algebra. We study the interrelation of them. We further study these concepts for the Cartesian product A × B of two function algebras.

View full abstract

We treat a zero-sum two-person game, what is called, a search game between the hider and the seeker, in which there is a cost for searching a region. If the seeker searches two regions, it is usual that the total cost for two regions is the sum of each cost for a region. However, there may be a saving of the setup cost for the second region when the seeker decides in advance two regions efficiently, and plans to change from one region to another region efficiently. If we take into mind this kind of saving, the cost may not be non-additive. In this paper, we analyze a search game when the cost is not necessarily additive.

View full abstract

The purpose of this paper is to study the notion of relative extreme amenability for pairs of topological groups. We give a characterization by a fixed point property on universal spaces. In addition we introduce the concepts of an extremely amenable interpolant as well as maximally relatively extremely amenable pairs and give examples. It is shown that relative extreme amenability does not imply the existence of an extremely amenable interpolant. The theory is applied to generalize results of [KPT05] relating to the application of Fra¨ıss´e theory to theory of Dynamical Systems. In particular, new conditions enabling to characterize universal minimal spaces of automorphism groups of Fra¨ıss´e structures are given.

View full abstract

We discuss the problem of shrinkage estimation for the autocovariance matrix of a Gaussian stationary vector-valued process to improve on the usual sample autocovariance matrix with respect to the mean squares error. We propose a kind of empirical Bayes estimators when the mean of the stochastic process is zero and non-zero. We show that the shrinkage estimators dominate the usual estimators, and the asymptotic risk differences are similar to that of scalar-valued Gaussian stationary processes. This result seems to be useful for the autocovariance estimation with vectorvalued dependent observations.

View full abstract

We prove that the free locally convex space L(X) over a metrizable space X has countable tightness if and only if X is separable.

View full abstract