The η-Invariant of Twisted Dirac Operators of S3/Γ

The aim of this paper is to compute the and ~-invariants for the Dirac operator of the quotient of the sphere S ³ by a finite subgroup, twisted by a representation of its fundamental group.     

Positive symmetric quotients and their selfadjoint extensions

We define a quotient of bounded operators and on a Hilbert space with a kernel condition as the mapping , . A quotient is said to be positive symmetric if . In this paper, we give a simple construction of positive selfadjoint extensions of a given positive symmetric quotient .

     

Conditional weak compactness in vector-valued function spaces

Let be an ideal of over a -finite measure space and let be the Köthe dual of with . Let be a real Banach space, and the topological dual of . Let be a subspace of the space of equivalence classes of strongly measurable functions and consisting of all those for which the scalar function belongs to . For a subset of for which the set is -bounded the following statement is equivalent to conditional -compactness: the set is conditionally -compact and is a conditionally weakly compact subset of for each , with . Applications to Orlicz-Bochner spaces are given.

     

An example of an asymptotically Hilbertian space which fails the approximation property

Following Davie's example of a Banach space failing the approximation property (1973), we show how to construct a Banach space which is asymptotically Hilbertian and fails the approximation property. Moreover, the space is shown to be a subspace of a space with an unconditional basis which is ``almost' a weak Hilbert space and which can be written as the direct sum of two subspaces all of whose subspaces have the approximation property.

     

Decreasing flow invariant sets and fixed points of quasimonotone increasing operators

In this paper, we obtain some new results about the existence of multiple fixed points of a kind of quasimonotone increasing operator by the new method of decreasing flow invariant set.

     

On a Class of Elliptic-Parabolic Equations on Unbounded Intervals

We study a class of degenerate elliptic second order differential operators acting on some polynomial weighted function spaces on [0,+[. We show that these operators are the generators of C ₀-semigroups of positive operators which, in turn, are the transition semigroups associated with right-continuous normal Markov processes with state space [0,+]. Approximation and qualitative properties of both the semigroups and the Markov processes are investigated as well. Most of the results of the paper depend on a representation of the semigroups we give in terms of powers of particular positive operators of discrete type we introduced and studied in a previous paper.     

Approximation of conjugate functions by generalized Abel-Poisson operators

We obtain a sharp value for the constant in the leading term of the deviation of a function belonging to the class Lip₁ α from the generalized Abel-Poisson operators specified by the summation factors of the conjugate Fourier series in the case 0 < α <l ≤ 1. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 595–602, April, 2000.     

Strong topologies on vector-valued function spaces

Let be a real Banach space and let E be an ideal of L ⁰ over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function , defined by , belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.     

On Nonlinear Integro-differential Operators in Generalized Orlicz–Sobolev Spaces

A nonlinear integral operator T of the form (Tf)(s)=∫_G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T.     

Preconditioned sor methods for generalized least-squares problems

1.IntroductionThegeneralizedleastsquaresproblem,definedasmin(Ax--b)"W--'(Ax--b),(1.1)xacwhereAERm",m>n,bERm,andWERm'misasymmetricandpositivedefinitematrix,isfrequentlyfoundwhensolvingproblemsinstatistics,engineeringandeconomics.Forexample,wegetgeneralizedleastsquaresproblemswhensolvingnonlinearregressionanalysisbyquasi-likelihoodestimation,imagereconstructionproblemsandeconomicmodelsobtainedbythemaximumlikelihoodmethod(of.[1,21).Paige[3,4]investigatestheproblemexplicitly.Hechangestheorig…