Canonical extension of actions of locally compact quantum groups

In this paper, we generalize the notion of the canonical extension of automorphisms of von Neumann algebras to the case of actions of locally compact quantum groups (in the sense of Kustermans and Vaes). Various expected properties will be shown to hold for this new canonical extension. As an application, we describe the flow of weights of the crossed product of a type III factor by some special action of a discrete Kac algebra.     

Banach空间上有界可逆线性变换逆变换的结构

Fillmore在[1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.     

A tall space with a small bottom

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if , then there is such a space of height with only many isolated points. This implies that there is a locally compact scattered space of height with isolated points in ZFC, solving an old problem of the first author.

     

The rank of finitely generated modules over group algebras

We show the existence of a rank function on finitely generated modules over group algebras , where is an arbitrary field and is a finitely generated amenable group. This extends a result of W. Lück (1998).

     

Hyperbolic mean growth of bounded holomorphic functions in the ball

We consider the hyperbolic Hardy class , . It consists of holomorphic in the unit complex ball for which and

where denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type -function and the area function are defined in terms of the invariant gradient of , and membership of is expressed by the property of the functions. As an application, we can characterize the boundedness and the compactness of the composition operator , defined by , from the Bloch space into the Hardy space .

     

TESTING DIFFERENT CONJUGATE GRADIENT METHODS FOR LARGE—SCALE UNCONSTRAINED OPTIMIZATION

In this PaPer we test different conjugate gradient (CG) methods for solving large-scale unconstrained optimization problems.The methods are divided in two groups:the first group includes five basic CG methods and the second five hybrid CG methods.A collection of medium-scale and large-scale test problems are drawn from a standard code of test problems.CUTE.The conjugate gradient methods are ranked according to the numerical results.Some remarks are given.     

On perturbations of matrix pencils with real spectra, a revisit

This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.

     

Stabilizability in Asymptotically Finite-Dimensional Semigroups

We study a semigroup of linear operators on a Banach space X which satisfies the condition codim X ₀<, where We show that X ₀ is closed and establish some properties of the asymptotic behavior of the subspaces complementing X ₀ to X.     

Invariant Euler–Lagrange Equations and the Invariant Variational Bicomplex

In this paper, we derive an explicit group-invariant formula for the Euler–Lagrange equations associated with an invariant variational problem. The method relies on a group-invariant version of the variational bicomplex induced by a general equivariant moving frame construction, and is of independent interest.     

The PDE-preserving operators on nuclearly entire functions of bounded type

The PDE-preserving operators O on the space of nuclearly entire functions of bounded type H_Nb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations. We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ, such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ. This revised version was published online in June 2006 with corrections to the Cover Date.