1. Introduction and notation. In this paper the word " local " is used in at least three different meanings. Our aim is to study local Banach spaces of Fréchet or other locally convex spaces, and it turns out that it is convenient to use the local theory of Banach spaces for this purpose. Recall that given a locally convex space E and a continuous seminorm p on E the completion of the normed sp...

SVM theory was originally developed on the basis of a separable binary classification problem, and other approaches have been later introduced. In this paper is demonstrated that all these approaches admit the same dual problem formulation. Let Z = ((x1, y1), . . . , (xn, yn)) = (z1, . . . , zn) ∈ (X × Y)n be a training set, where X is the input space and Y = {θ1, θ2} = {−1, +1} the output spac...

We investigate the existence of well-ordered sequences of Baire 1 functions on separable metric spaces. Any set F of real valued functions defined on an arbitrary set X is partially ordered by the pointwise order, that is f ≤ g iff f(x) ≤ g(x) for all x ∈ X. In other words put f < g iff f(x) ≤ g(x) for all x ∈ X and f(x) 6= g(x) for at least one x ∈ X. Our aim will be to investigate the possibl...

We propose a solution to a problem that is encountered in defining a notion of full meet base revision, ensuring that the output can always be re-used as an input. For this purpose, we introduce the concept of a separable belief base and show that separable bases are exactly those for which the full meet revision closure operator satisfies the extended set of A. G. M. postulates. We then define...

Let {Xn, n > 1} be a sequence of coordinatewise negatively associated random vectors taking values in a real separable Hilbert space with the kth partial sum Sk, k > 1. We provide conditions for the convergence of ∑∞ n=1 1 n P(max16k6n ‖Sk‖ > εn α) and ∑∞ n=1 logn n P(max16k6n ‖Sk‖ > εn α) for all ε > 0. The converses of these results are also discussed.

We investigate the concept of cylindrical Wiener process subordinated to a strictly α–stable Lévy process, with α∈(0,1), in an infinite–dimensional, separable Hilbert space, and consider related stochastic convolution. then introduce corresponding Ornstein–Uhlenbeck focusing on regularizing properties Markov transition semigroup defined by it. In particular, we provide explicit, original formul...

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are Rn, Cn, (separable) Hilbert space and more generally all separable Banach spaces, the Cantor space 2N, the Baire space NN, the infinite symmetric group S∞...

A well known argument of James yields that if a Banach space X contains `1 ’s uniformly, then X contains `1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal `1-indices of Bourgain. In the second half we use our results to calculate the `1-index of certain Banach spaces. Furthermore we show that the `1-index of a separable Banach space not containing `1 ...

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .