We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

We extend the Gaussian scale mixture model of dependent subspace source densities to include non-radially symmetric densities using Generalized Gaussian random variables linked by a common variance. We also introduce the modeling of skew using the Normal Variance-Mean mixture model. We give closed form expressions for likelihoods and parameter updates in the EM algorithm.

Abstract In this paper, we will investigate some topological properties of Rb set of all bounded generalized Rhally matrices given by b sequences in H. We will show that Rb is closed subspace of B (H) and we will define an operator from T to Rb and show that this operator is injective and continuous in strong-operator topology.

This is a survey over recent asymptotic results on random polytopes in d-dimensional Euclidean space. Three ways of generating a random polytope are considered: convex hulls of finitely many random points, projections of a fixed highdimensional polytope into a random d-dimensional subspace, intersections of random closed halfspaces. The type of problems for which asymptotic results are describe...

The notion of an invariant subspace is fundamental to the subject of operator theory. Given a linear operator T on a Banach space X, a closed subspace M of X is said to be a non-trivial invariant subspace for T if T (M) ⊆M and M 6= {0}, X. This generalizes the idea of eigenspaces of n×n matrices. A famous unsolved problem, called the “invariant subspace problem,” asks whether every bounded line...

Subspace clustering methods based on `1, `2 or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, `1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from diffe...

This paper considers the automatic design of fuzzy rule-basedclassification systems based on labeled data. The classification performance andinterpretability are of major importance in these systems. In this paper, weutilize the distribution of training patterns in decision subspace of each fuzzyrule to improve its initially assigned certainty grade (i.e. rule weight). Ourapproach uses a punish...

If a nonnegative selfadjoint linear relation A in Hilbert space and closed subspace S are assumed to satisfy that the domain of is invariant under orthogonal projector onto S, then admits particular matrix representation with respect decomposition S⊕S⊥. This used give explicit formulae for Schur complement on as well S-compression A.

We study positive shadowing and chain recurrence in the context of linear operators acting on Banach spaces or even normed vector spaces. show that for there is only one recurrent set, this set a closed invariant subspace. prove every transitive dynamical system with property frequently hypercyclic and, as corollary, we obtain hypercyclic.

Introduction: In the recent decade, there have been significant efforts in developing multiuser detection technologies to alleviate the effect of multiple access interference (MAI) in codedivision multiple-access (CDMA) systems. Blind multiuser detection is of special interest for MAI mitigation in CDMA systems since it is impractical to assume perfect knowledge of parameters such as spreading ...