算子代数上保因子的可加映射
发布时间：2018-11-21 17:03
【摘要】：本文主要研究了无限维Banach空间上标准算子代数之间双边保左(或右)因子和因子的可加满射以及无限维复Hilbert空间上全体有界线性算子代数之间双边保左(或右)*因子的可加满射,得到了以下主要结果.1.可加满射Φ：A→B(其中A,B分别是作用在无限维复Banach空间x,y上的标准算子代数)双边保左(或右)因子当且仅当存在可逆有界线性或共轭线性算子U：x→y和V：y→x使得对任意T∈A,有Φ(T)=UTV.2.Φ：A→B是可加满射,则Φ双边保因子当且仅当下列形式之一成立：(1)存在有界可逆线性或共轭线性算子U：x→y和V：y→x使得对任意T∈A,有Φ(T)=VTV;(2)x和y是自反Banach空间,且存在有界可逆线性或共轭线性算子V：x*→y和V：y→x使得对任意T∈A,有Φ(T)=UT*V.3.令H和K是无限维复Hilbert空间,Φ是从B(H)到B(K)上的可加满射,则Φ双边保左(右)*因子的充分必要条件是存在非零复数λ和有界可逆线性或共轭线性算子U：H→K使得对任意的T∈B(H),都有Φ(T)=λUTU*.
[Abstract]:In this paper, we study the bilateral left (or right) preserving left (or right) factors and factors between standard operator algebras on infinite dimensional Banach spaces and the left (or right) bilateral preserving left (or right) among all bounded linear operator algebras on infinite dimensional complex Hilbert spaces. * the additive surjection of a factor, The following main results are obtained. 1. The additive surjection 桅: a is B (where AZB is acting on an infinite dimensional complex Banach space x, respectively). Standard operator Algebras on y) bilateral preserving left (or right) factors if and only if there are invertible or conjugate linear operators U: x and V: y such that for any T 鈭，
本文编号：2347624
[Abstract]:In this paper, we study the bilateral left (or right) preserving left (or right) factors and factors between standard operator algebras on infinite dimensional Banach spaces and the left (or right) bilateral preserving left (or right) among all bounded linear operator algebras on infinite dimensional complex Hilbert spaces. * the additive surjection of a factor, The following main results are obtained. 1. The additive surjection 桅: a is B (where AZB is acting on an infinite dimensional complex Banach space x, respectively). Standard operator Algebras on y) bilateral preserving left (or right) factors if and only if there are invertible or conjugate linear operators U: x and V: y such that for any T 鈭，
本文编号：2347624
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