Representations approchees d'un groupe dans une algebre de banach

Let T be a continuous map from a compact group G to the group of invertible bounded linear operators on a Hilbert space H, the latter being endowed with the norm topology. If the norms T(gh)-T(g)T(h) are small enough (g,h G), we show that T is a small perturbation of some norm continuous representation of G on H.     

On the Range of the Aluthge Transform

Let be the algebra of all bounded linear operators on a complex separable Hilbert space For an operator let be the Aluthge transform of T and we define for all where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range of Δ. We prove that R(Δ) is neither closed nor dense in However R(Δ) is strongly dense if is infinite dimensional. An erratum to this article is available at .     

Characterization of cores of assignment games

We consider the assignment game of Shapley and Shubik (1972). We prove that the class of possible cores of such games (expressed in terms of payoffs for players on one side of the market) is exactly the same as a special class of polytopes, called 45-lattices. These results parallel similar work done by Conway (in Knuth, 1976) and Blair (1984) for marriage markets.Research supported by the Office of Naval Technology.     

The closure of unitary orbit for strongly irreducible operators in a class of nest algebras

A linear operatorT L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let be a nest with infinite dimensional atoms, be the nest algebra associated with and be the closure of , then the following result is proved

Contractions with a unilateral shift summand are reflexive

If T is a contraction on the Hilbert space H and there is an invariant subspace K for T such that T/K is similar to a backward shift, then T is reflexive. If similarity is replaced by quasi-similarity, then the same conclusion holds under the additional condition that the defect index of T be finite.This research was partially supported by National Science Council (Republic of China).     

Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems

We derive a posteriori error estimates for fully discrete approximations to solutions of linear parabolic equations. The space discretization uses finite element spaces that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto. We derive novel a posteriori estimates for the norms of and the higher order spaces, and , with optimal orders of convergence.

     

Estimates for multilinear singular integral operators with nonsmooth kernels

Let (, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we consider the behavior on × ⋯ × for the m-linear singular integral operators with nonsmooth kernels which were first introduced by Duong, Grafakos and Yan.     

Field dependence of magnetoresistance in epitaxial single-crystal La2/3Ca1/3MnO3-δ thin film

Epitaxial La_2/3Ca_1/3MnO₃ thin films were prepared on NdGaO₃(1lO) substrates by d.c. magnetron sputtering method. The measurements of magnetoresistance ρ(H) upon magnetic field at different temperatures were carried out in the field range of 0–8 T. It is found that ρ(H) obeys the following relations: when the temperature (T) is higher than the Curie temperature below and whenT is far WowT _c. It is suS8ested that the negative magnetoresistive effect is mainly due to enhancement of the magnetoconductance. Project supported by the National Natural Science Foundation of China (Grant No. 19504012) and the Chinese Academy of Sciences.     

Automorphisms of the Hatcher-Thurston complex

Let S be a compact, connected, orientable surface of positive genus. Let be the Hatcher-Thurston complex of S. We prove that Aut is isomorphic to the extended mapping class group of S modulo its center. The first author is supported by a Rackham Faculty Fellowship, Horace H. Rackham School of Graduate Studies, University of Michigan. The second author is supported in part by the Turkish Academy of Sciences under the Young Scientists Award Program (MK/TüBA-GEBİP 2003-10).     

Approximate Unitary Equivalence to Skew Symmetric Operators

An operator \(T\) on a complex Hilbert space \(\mathcal {H}\) is called skew symmetric if \(T\) can be represented as a skew symmetric matrix relative to some orthonormal basis for \(\mathcal {H}\) . In this paper, we study the approximation of skew symmetric operators and provide a \(C^*\) -algebra approach to skew symmetric operators. We classify up to approximate unitary equivalence those skew symmetric operators \(T\in \mathcal {B(H)}\) satisfying \(C^*(T)\cap \mathcal {K(H)}=\{0\}\) . This is used to characterize when a unilateral weighted shift with nonzero weights is approximately unitarily equivalent to a skew symmetric operator.     

On the extension principle in internal set theory

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 66–78, November–December, 1992.     

The uniqueness of the adjoint operation I

Let H be a complex, infinite-dimensional Hilbert space. Let B(H) denote the set of bounded linear operators on H. This paper contains a nonlinear characterization of the adjoint operation on B(H). The statement of this result is:THEOREM:Let h: B(H) B(H)be a function such that h(I)0.Then h(ST)=h(T)h(S)and h(S)S0for all elements Sand Tof B(H)if and only if h(S)=S^* for all S B(H).     

A Note on Primes and Goldbach Numbers in Short Intervals

Let J(N, H) be the Selberg integral and E(x, T) the error term in Kaczorowski-Perelli's weighted form of the classical explicit formula. We prove that the estimate J(N, H) = o(H2 N) is connected with an appropriate estimate of _N ^2N| E(x,T)² dx, uniformly for H and T in some ranges. Moreover, assuming a suitable bound for _N ^2N| E(x,T)|² dx, we also obtain, for all sufficiently large N and H (log N)11/12, that every interval [N,N + H] contains H Goldbach numbers.     

Linear maps preserving the set of Fredholm operators

Let be an infinite-dimensional separable complex Hilbert space and the algebra of all bounded linear operators on . In this paper we characterize surjective linear maps preserving the set of Fredholm operators in both directions. As an application we prove that preserves the essential spectrum if and only if the ideal of all compact operators is invariant under and the induced linear map on the Calkin algebra is either an automorphism, or an anti-automorphism. Moreover, we have, either or for every Fredholm operator .

     

Algebras generated by a weighted shift

Techniques of Olin and Thomson and of Chevreau, Pearcy and Shields are used to prove the following: If T is an injective weighted shift on H with r(T)=T then for each L (a(T), weak-*)^*, there exist f, g H so that L(A)=Af, g for all A a(T). Thus the map i(A)=A is a homeomorphism from (a(T), weak-*) onto (a(T), WOT).     

Maximal monotonicity, conjugation and the duality product

Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.

The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.

     

Brownian bridges on Riemannian manifolds

We study properties of Brownian bridges on a complete Riemannian manifoldM. LetQ _x,y ^t be the law of Brownian bridge fromx toy with lifetimet. Q _x,y ^t is a probability measure on the space _x,y of continuous paths with (0)=x and (1)=y. We prove thatQ _x,y ^t possesses the large deviation property with the rate function

A geometric approach to the cascade approximation operator for wavelets

This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let be a Hilbert space, and let be a representation ofL ( ) on . LetR be a positive operator inL ( ) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on (bounded, but noncontractive) such that