Pontrjagin空间上的第一类算子代数  

THE OPERATOR ALGEBRA OF CLASS I ON PONTRJAGIN SPACE

作　　者：杨海涛[1] 

机构地区：[1]厦门理工学院数理系,厦门361024

出　　处：《系统科学与数学》2013年第8期993-1006,共14页Journal of Systems Science and Mathematical Sciences

基　　金：福建省自然科学基金资助课题(2007J0193)

摘　　要：对Π_k空间上有单位的第一类闭算子代数,在正规分解∏_k=(ZH)+Z~*下给出一般形式如下A={((M)A12M+M0TA23(M*)*)︱M0∈ker,M=(M)},其中A_(12)=(q(M~*)+q(M_0~*)YPU)ε,A_(23)=η(q(M)+q(M_0)ZU),M∈B/ker,是在类M中只取一个代表元的映射;Y Z∈R,U∈D,Υ∈Τ,Τ■B(Z~*,Z)是对称的线性子空间.B=A_(|H)■B(H),是C*-代数;R■H^k是对B^k不变的闭子空间,:B→B(Z)是一个同态,q:ker→H^(k)是*-闭的拟向量;D,R;{q(Mo)|M_0∈ker}相互直交,D■ker,(M)~TU=MU;P是自共轭线性闭算子,p^2=I.满足:(Y,Z),(PU,U),(q(M_1),q(M_2)),(M)T∈Τ,T∈Τ,M_1,M_2,M∈B.Let .4 be a closed unital operator algebra of class I with property A（1, 3） on ∏k space, Z is neutral invariant subspace of .A, and dimZ = k. Then with the normal decomposition Пk=（Z＋H）＋Z^＊ the general form of algebra ,4 has following form A={（φ（M） A12 T M＋M0 A23 φ（M^＊）^）｜M0∈kerφ,M=ψ_～（M）｜}where A12=（q（M^＊）＋q（M0^＊））＋Y＋PU）×ξ,A23=η（q（M））＋q（M0）＋Z＋U）,^～M∈B/kerφ,ψis a map that takes only one representative element in c!ass Y,Z∈R,U∈D,T∈T,T∪→-B（Z^＊,Z）is a symmetric linear subspace.B=A｜H∪→-B（H）is aC＊--algebra;R∪→-H^kis a closed invariant subspace for B^k,φ：B→B（Z）is a homo-morphism,q：kerφ→H（k）is a＊-closed quasi-vector;D,R,{q（M0）｜M0∈kerφ}are orthogonal, mutually;D∪→-kerφ,φ（M）^TU=MU;P is a closed self-conjugate linear operator,P^2=I and such that（Y,Z）,（PU,U）,（q（M1）,q（M2））,φ（M）T∈T,T∈T,M1,M2,M∈B.

关 键 词：PONTRJAGIN空间 算子代数 第一类代数 代数形式 

分 类 号：O177[理学—数学]