In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.

In the paper, we define a notion of prereflexivity for subspaces, give several equivalent conditions of this notion and prove that if $ C_ L(H) is prereflexive, then every aweakly closed subspace of S is prereflexive if and only if $ has the property WP(see definition 2.11). By our result, we construct a reflexive operator A such that A 0 is not prereflexive.

It follows from [1] and [7] that any closed n-codimensional subspace (n ≥ 1 integer) of a real Banach space X is the kernel of a projection X → X, of norm less than f(n) + ε (ε > 0 arbitrary), where f(n) = 2 + (n − 1) √ n + 2 n + 1 . We have f(n) < √ n for n > 1, and f(n) = √ n − 1 √ n + O (

We give a general overview of the state-of-the-art in subspace system identification methods. We have restricted ourselves to the most important ideas and developments since the methods appeared in the late eighties. First, the basis of linear subspace identification are summarized. Different algorithms one finds in literature (Such as N4SID, MOESP, CVA) are discussed and put into a unifyin...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

In this paper we show how to embed the variable internal structure present in square implicit descriptions inside an (A, E, B) invariant subspace contained in the kernel of the output map. Thanks to this embedding, we make unobservable the variable internal structure, obtaining in this way a proper closed loop system with a controllable pre speciÞed structure. Copyright c ° 2002 IFAC.

If X is a closed subspace of a Banach space L which embeds into a Banach lattice not containing l ∞ ’s uniformly and L/X contains l ∞ ’s uniformly, then X cannot have local unconditional structure in the sense of Gordon-Lewis (GLl.u.st.). 1991 Mathematics Subject Classification. 46B03, 43A46.

Let X be a Banach space, (I, μ) be a finite measure space, and Φ be an increasing subadditive continuous function on [0,+∞) with Φ(0) = 0. In the present paper, we discuss the best p-simultaneous approximation of L(I,G) in L(I,X) where G is a closed subspace of X .

We study the completeness properties of the set of wavelets in L2(R). It is well-known that this set is not closed in the unit ball of L2(R). However, if one considers the metric inherited as a subspace (in the Fourier transform side) of L2(R, dξ) ∩ L(R∗, dξ |ξ| ), we do obtain a complete metric space.