套代数模上的线性保秩映射

主要讨论作用在复Hilbert空间弱闭 AlgN-模上的线性保秩映射，并给出在各种情况下保秩一性线性映射的刻画．作为应用，最后讨论了弱闭 AlgN-模上的模同构，并得出这样的同构是平凡的．     

套代数上的Lie三重同构（英文）

设N,M是复可分Hilbert空间H上的套,7(N),7(M)是相应的套代数.本文证明了Lie三重同构L:τ(N)→7(M)具有形式L(x)=θ(x)+h(x),其中θ是同构或负的反同构,h:τ(N)→CI是线性映射,使得对任意的x,y,z∈7(N),h([x,y],z])=0.     

关于相关系间的同构映射

建立了相关系间的同构映射,给出了相关系间同构映射的一些等价条件,并通过具体的同构映射揭示出相关系的一些内在本质.     

保持谱半径的乘法映射

设X和Y为无限维Banach空间,Φ：B（X）→B（Y）是保持谱半径的满射,且秩为1算子,则Φ具有形式Φ（T）=ATA∧-1,这里A：X→Y或是线性拓扑同构映射或是线性拓扑同构映射的共轭。     

C~*-代数的实完全等距映射

C*-代数的*-同构一定是(完全)等距映射,反之不然.本文证明了C*-代数的实完全等距映射能够完全决定C*-代数*-同构的结论.     

遗传算法、差分演化和一个处理约束的映射

S.Koziel和Z.Michalewicz(1999年)提出了一个处理约束的映射,研究该映射与不同算法相结合后的不同的代数结构.从理论上证明了当其与遗传算法相结合时,该映射是同构映射,而在差分演化算法的变异操作下,该映射不是同态映射,更不是同构映射.进而表明,该映射更适宜于与遗传算法相结合,而并不太适宜于与差分演化算法(及其类似的算法)相结合。     

B(X)上保持算子拟仿射性或值域稠性的线性映射

设X和y是无限维的复Banach空间,φ是从B(X)到B(y)保单位的线性满射.本文证明了φ双边保算子的拟仿射性当且仅当φ为同构或反同构;φ双边保算子的值域稠性当且仅当φ是同构.     

B(X)上保持算子拟仿射性或值域稠性的线性映射

设X和Y是无限维的复Banach空间,Φ是从B(X)到B(Y)保单位的线性满射.本文证明了Φ双边保算子的拟仿射性当且仅当Φ为同构或反同构;Φ双边保算子的值域稠性当且仅当Φ是同构.     

一类周期全纯自同构的线性化

该文证明了一类周期全纯自同构映射与线性映射同构，而由这类全纯自同构映射生成的子群在犃狌狋Ｃｎ 中是稠密的．     

因子von Neumann代数中套子代数上Jordan同构的刻画

本文研究了套子代数上由零积确定的子集中保Jordan积的线性映射与同构和反同构的关系.证明了若对任意的A,B∈algMβ且AB=0,有Φ(A■B)=Φ(A)■Φ(B)成立,则Φ是同构或反同构.其中,algMβ,algMγ是因子von Neumann代数M中的两个非平凡套子代数,Φ:algMβ→algMγ是一个保单位线性双射.     

A surjectivity theorem for differential operators on spaces of regular functions

In this article we show that it is possible to construct a Koszul-type complex for maps given by suitable pairwise commuting matrices of polynomials. This result has applications to surjectivity theorems for constant coefficients differential operators of finite and infinite order. In particular, we construct a large class of constant coefficients differential operators which are surjective on the space of regular (or monogenic) functions on open convex sets.     

Linear maps preserving the isomorphism class of lattices of invariant subspaces

Let be an -dimensional complex linear space and the algebra of all linear transformations on . We prove that every linear map on , which maps every operator into an operator with isomorphic lattice of invariant subspaces, is an inner automorphism or an inner antiautomorphism multiplied by a nonzero constant and additively perturbed by a scalar type operator. The same result holds if we replace the lattice of invariant subspaces by the lattice of hyperinvariant subspaces or the set of reducing subspaces. Some of these results are extended to linear transformations of finite-dimensional linear spaces over fields other than the complex numbers. We also characterize linear bijective maps on the algebra of linear bounded operators on an infinite-dimensional complex Hilbert space which have similar properties with respect to the lattice of all invariant subpaces (not necessarily closed).

     

The reflection effect for constant risk averse agents

Assume a decision maker has a preference relation over monetary lotteries. The reflection effect, first observed by Kahneman and Tversky, states that the preference order for two lotteries is reversed once they are multiplied by −1. The decision maker is constant risk averse (CRA) if adding the same constant to two distributions, or multiplying them by the same positive constant, will not change the preference relation between them. We combine these two axioms with the betweenness axiom and continuity, and prove a representation theorem. A technical curiosity is that the functions we get satisfy the betweenness axiom, yet are not necessarily Gâteaux (nor Fréchet) differentiable.     

Random iterations of holomorphic maps in complex Banach spaces

Conditions guaranteeing the uniform convergence to constant maps of random iterations of holomorphic contractions on unbounded domains in complex Banach spaces are established.

     

Image multiple point spaces and rectified homotopical depth

We investigate the local topology of multiple point spaces in the image of a finite complex analytic map. In particular, we find examples of maps for which the constant sheaf on an image multiple point space of the map is perverse. These results are proved by the use of a spectral sequence which calculates the homology of the image of a continuous map.

     

Minimax theorems for set-valued maps without continuity assumptions

We introduce several classes of set-valued maps with new generalized convexity properties. We also obtain minimax theorems for set-valued maps which satisfy these convexity assumptions and which are not continuous. Our method consists of the use of a fixed point theorem for weakly naturally quasiconcave set-valued maps, defined on a simplex in a topological vector space, or of a constant selection of quasiconvex set-valued maps.     

An explicit Berry-Esséen bound for uniformly expanding maps on the interval

For uniformly expanding maps on the interval, analogous versions of the Berry-Esséen theorem are known but only with an unexplicit upper bound in O(1/\(\sqrt n \)) without any constants being specified. In this paper, we use the recent complex cone technique to prove an explicit Berry-Essén estimate with a reasonable constant for these maps. Our method is not limited to maps on the interval however, and should apply to many situations.     

Cramér-Rao bound for estimates of frequencies and damping factors of real superimposed signals with multiple poles in noise

The problem of estimating frequencies and damping factors of real superimposed signals with multiple poles in white Gaussian noise is considered. Such signals are described by real quasipolynomials, i.e. by linear combinations of real damped sinusoids multiplied by power functions. In a particular case when poles are simple, a real quasipolynomial becomes a real damped sinusoid. An explicit expression of the Cramér-Rao bound (CRB) for the estimation of frequencies and damping factors of the signals is obtained. To derive the CRB, we use the expression for the Fisher information matrix (FIM) which we obtained in a previous paper for the model of complex quasipolynomials (i.e. complex exponentials multiplied by complex polynomials). We rewrite the model of real quasipolynomials as a model of complex quasipolynomials with constraints imposed on the parameter set. Then we make use of the formula presented by Gorman and Hero that allows us to obtain the CRB for the model with constraints from the FIM for the model without constraints. The results of numerical simulations are presented and discussed.     

Mean value conjectures for rational maps

Let p be a polynomial in one complex variable. Smale's mean value conjecture estimates |p′(z)| in terms of the gradient of a chord from (z,?p(z)) to some stationary point on the graph of p. The conjecture does not immediately generalize to rational maps since its formulation is invariant under the group of affine maps, not the full Möbius group. Here we give two possible generalizations to rational maps, both of which are Möbius invariant. In both cases we prove a version with a weaker constant, in parallel to the situation for Smale's mean value conjecture. Finally, we discuss some candidate extremal rational maps, namely rational maps all of whose critical points are fixed points.     

Associated families of pluriharmonic maps and isotropy

Like minimal surface immersions in 3-space, pluriharmonic maps into symmetric spaces allow a one-parameter family of isometric deformations rotating the differential (“associated family”); in fact, pluriharmonic maps are characterized by this property. We give a geometric proof of this fact and investigate the “isotropic” case where this family is constant. It turns out that isotropic pluriharmonic maps arise from certain holomorphic maps into flag manifolds. Further, we also consider higher dimensional generalizations of constant mean curvature surfaces which are Kähler submanifolds with parallel (1,1) part of their soecond fundamental form; under certain restrictions there are also characterized by having some kind of (“weak”) associated family. Examples where this family is constant arise from extrinsic Kähler symmetric spaces.