【摘要】：本文主要研究了無限維Banach空間上標(biāo)準(zhǔn)算子代數(shù)之間雙邊保左(或右)因子和因子的可加滿射以及無限維復(fù)Hilbert空間上全體有界線性算子代數(shù)之間雙邊保左(或右)*因子的可加滿射,得到了以下主要結(jié)果.1.可加滿射Φ：A→B(其中A,B分別是作用在無限維復(fù)Banach空間x,y上的標(biāo)準(zhǔn)算子代數(shù))雙邊保左(或右)因子當(dāng)且僅當(dāng)存在可逆有界線性或共軛線性算子U：x→y和V：y→x使得對(duì)任意T∈A,有Φ(T)=UTV.2.Φ：A→B是可加滿射,則Φ雙邊保因子當(dāng)且僅當(dāng)下列形式之一成立：(1)存在有界可逆線性或共軛線性算子U：x→y和V：y→x使得對(duì)任意T∈A,有Φ(T)=VTV;(2)x和y是自反Banach空間,且存在有界可逆線性或共軛線性算子V：x*→y和V：y→x使得對(duì)任意T∈A,有Φ(T)=UT*V.3.令H和K是無限維復(fù)Hilbert空間,Φ是從B(H)到B(K)上的可加滿射,則Φ雙邊保左(右)*因子的充分必要條件是存在非零復(fù)數(shù)λ和有界可逆線性或共軛線性算子U：H→K使得對(duì)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，

本文編號(hào)：2347624