A type of oscillation modeled on BMO is introduced to characterize norm compactness in L 1. This result is used to characterize the bounded linear operators from L 1 into a Banach space X that map weakly convergent sequences onto norm convergent sequences (i.e. are Dunford-Pettis). This characterization is used to study the geometry of Banach spaces X with the property that all bounded linear o...

It is well-known that an operator in a finite-dimensional vector space is uniquely determined up to a similarity by its Jordan model. Given an operator T , two invariant subspaces M and N of T are said to be similar if there exists an invertible operator X such that XT = TX and XM = N . Clearly this is an equivalence relation in the lattice of invariant subspaces of T . Our paper was originally...

This paper deals with a class of morphological operators called connected operators These operators interact with the signal by merging at zones As a result they do not create any new contours and are very attractive for ltering tasks where the contour information has to be preserved This paper focuses on a class of operators dealing with motion information They remove from the original sequenc...

In this paper we study the action of the Binomial and Invert (interpolated) operators on the set of linear recurrent sequences. We prove that these operators preserve this set, and we determine how they change the characteristic polynomials. We show that these operators, with the aid of two other elementary operators (essentially the left and right shifts), can transform any impulse sequence (a...

In this paper, we prove that every multiplier M (i.e. every bounded operator commuting whit the shift operator S) on a large class of Banach spaces of sequences on Z is associated to a function essentially bounded by ‖M‖ on spec(S). This function is holomorphic on ◦ spec(S), if ◦ spec(S) 6= ∅. Moreover, we give a simple description of spec(S). We also obtain similar results for Toeplitz operato...

For a sequence {Tn} of continuous linear operators on a separable Fréchet space X, we discuss necessary conditions and sufficient conditions for {Tn} to be topologically mixing, and the relations between topological mixing and the Hypercyclicity Criterion. Among them are: 1) topological mixing is equivalent to being hereditarily densely hypercyclic; 2) the Hypercyclicity Criterion with respect ...

The index theory for the space of finite propagation unitary operators was developed by Gross, Nesme, Vogts and Werner from viewpoint quantum walks in mathematical physics. In particular, they proved that $\pi_0$ is determined index. However, nothing known about higher homotopy groups. this article, we describe type on Hilbert square summable $\mathbb{C}$-valued $\mathbb{Z}$-sequences, so can d...

In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...

let $(u_n)$ be a sequence of fuzzy numbers.  we recover the slow oscillation of $(u_n)$ of fuzzy numbers from the ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. further, fuzzy analogues of some well known classical tauberian theorems for ces`{a}ro summability method are established as particular cases.