A polynomial space proof of the Graham-Pollak theorem

This note describes a polynomial space proof of the Graham-Pollak theorem.     

A mean ergodic theorem on vector spaces

A mean ergodic theorem for a matrix is first proved from which a mean ergodic theorem for affine operators on a vector space without any topological structure is obtained.     

Order shattering and Wilson''s theorem

The notion of order shattering was introduced in Anstee et al. (Graphs Combin. 18 (2002) 59–73). Here, we pursue further the algebraic interpretation that was established there. With this tool we give a new proof and a generalization for Wilson's theorem on the diagonal form for the incidence matrices of t-subsets vs. k-subsets (European J. Combin. 11 (1990) 609–615). This allows a generalization of the corresponding rank formula modulo p, where p is an arbitrary prime.     

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.

     

Best proximity pair theorem in metrizable topological vector spaces

The object of this paper is to prove an existence result on best proximity pair. For this purpose, the class of factorizable multifunctions in approximately weakly compact, convex subset of metrizable topological vector space is used. As consequence, our theorem generalizes the result of Basha and Veeramani^[10]. Finally, certain known results have also been obtained as corollaries in this work.     

The Levin-Golovin theorem for sobolev spaces

We obtain sufficient conditions for the basis property of the family of exponentials

An existence theorem for Lagrange problems in Banach spaces

We give an existence theorem for a Lagrange problem in a reflexive separable Banach space. We prove the main theorem by means of the direct method of the calculus of variations introduced by Tonelli.This work has been supported by the Laboratorio per la Matematica Applicata, Consiglio Nazionale delle Ricerche, Genova, Italy.The authors wish to thank Professor J. P. Cecconi who has drawn their attention to these problems.     

Algebras in matrix spaces with displacement structure

We introduce the problem of the location of the algebras contained in a matrix space with displacement structure. We present some partial solutions of the problem that unify and generalize various results obtained so far for the spaces of Toeplitz, Loewner and Toeplitz plus Hankel matrices.     

An embedding theorem for Lie algebras

In this paper we give a sufficient condition for a restricted enveloping algebra to be quasi-elementary. We also prove that every finite dimensional -nilpotent Lie algebra can be embedded in a finite dimensional -nilpotent quasi-elementary Lie algebra.

     

The projective method for solving linear matrix inequalities

Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.     

Individual ergodic theorem for unitary maps of random matrices

Using simple techniques of finite von Neumann algebras, we prove a limit theorem for random matrices.

     

The Gauss-Bonnet theorem for vector bundles

We give a short proof of the Gauss-Bonnet theorem for a real oriented Riemannian vector bundle E of even rank over a closed compact orientable manifold M. This theorem reduces to the classical Gauss-Bonnet-Chern theorem in the special case when M is a Riemannian manifold and E is the tangent bundle of M endowed with the Levi-Civita connection. The proof is based on an explicit geometric construction of the Thom class for 2-plane bundles. Dedicated to the memory of Philip Bell Research partially supported by NSF grant DMS-9703852.     

Asymptotic results of Leray-type solutions of MHD systems

In this paper, we study the weak convergence of “Leray-type” solutions of a magneto-hydro-dynamic systems. The proofs are based on weak compactness arguments and linear algebra methods.     

Summability results for operator matrices on topological vector spaces

Basic summability results are established for matrices of linear and some nonlinear mappings between topological vector spaces.     

The Kreps-Yan theorem for Banach ideal spaces

Consider a closed convex cone C in a Banach ideal space X on some measure space with σ-finite measure. We prove that the fulfilment of the conditions C∩X ₊ = {0} and C??X ₊ guarantees the existence of a strictly positive continuous functional on X whose restriction to C is nonpositive.