Projective Completions of Jordan Pairs,Part II: Manifold Structures and Symmetric Spaces

We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields , and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generalizes the well-known (finite or infinite-dimensional) bounded symmetric domains as well as their ‘compact-like’ duals. An interpretation of such geometries as models of Quantum Mechanics is proposed, and particular attention is paid to geometries that might be considered as ‘standard models’ – they are associated to associative continuous inverse algebras and to Jordan algebras of hermitian elements in such an algebra.Mathematics Subject Classiffications (2000). primary: 17C36, 46H70, 17C65; secondary: 17C30, 17C90     

The algebraic structure ofH-dissipative operators in a finite-dimensional space

We study properties of Jordan representations ofH-dissipative operators in a finite-dimensional indefiniteH-space. An algebraic proof is given of the fact that such operators always have maximal semidefinite invariant subspaces. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 163–169, February, 1998. The authors axe grateful to Professor A. A. Shkalikov for useful discussions. The research of the first author was supported by INTAS under grant No. 93-0249. The research of the second author was supported by the International Science Foundation and the Russian Government under grant No. NZP300.     

Jordan李超代数的一些性质

代数A称为不可分解的,如果A不能分解成理想的直和.证明了满足C(L_o)=C(L)={0}的Jordan李超代数L一些重要性质.     

广义谱分解与亏损矩阵幂的算法

提出了亏损矩阵广义谱分解概念,所得广义特征矩阵具有类似若当链的性质AA(h)i=λiA(h)i+A(h+1)i.亏损矩阵可分解成A=∑si=1(λiA(0)i+A(1)i),由Am=∑si=1∑mh=0Chmλm-hiA(h)i可生成线性方程组,求出各A(h)i,进而计算A的较大次幂Am.介绍了广义谱分解在计算矩阵幂级数中的应用.     

Jordan标准型过渡矩阵的一种新算法

本文通过矩阵函数微分的相关知识,给出了 Jordan标准型过渡矩阵的一种新算法.     

Jordan triple derivations on J-subspace lattice algebras

Let L be a J-subspace lattice on a Banach space X and Alg L the associated J-subspace lattice algebra. Let A be a standard operator subalgebra (i.e., it contains all finite rank operators in AlgL) of AlgL and M■B(X) the Alg L-bimodule. It is shown that every linear Jordan triple derivation from A into M is a derivation, and that every generalized Jordan (triple) derivation from A into M is a generalized derivation.     

An eigenvalue problem for derogatory matrices

A matrix A is called derogatory   if there is more than one Jordan submatrix associated with an eigenvalue λ$\lambda$. In this paper, we are concerned with the eigenvalue problem of this type of matrices.