山东大学学报(理学版)
山東大學學報(理學版)
산동대학학보(이학판)
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2014年
2期
42-45
,共4页
值域%核%包含关系%可加映射
值域%覈%包含關繫%可加映射
치역%핵%포함관계%가가영사
range%kernel%inclusion%additive maps
设B( X)是无限维复Banach空间X上有界线性算子全体组成的Banach代数。研究了B( X)上双边保持值域(或核)包含关系的可加满射。设φ是B( X)上双边保持值域(或核)包含关系的可加满射,则存在X上的可逆有界线性或者共轭线性算子U和V使得橙T∈B( X),有φ( T)=UTV。
設B( X)是無限維複Banach空間X上有界線性算子全體組成的Banach代數。研究瞭B( X)上雙邊保持值域(或覈)包含關繫的可加滿射。設φ是B( X)上雙邊保持值域(或覈)包含關繫的可加滿射,則存在X上的可逆有界線性或者共軛線性算子U和V使得橙T∈B( X),有φ( T)=UTV。
설B( X)시무한유복Banach공간X상유계선성산자전체조성적Banach대수。연구료B( X)상쌍변보지치역(혹핵)포함관계적가가만사。설φ시B( X)상쌍변보지치역(혹핵)포함관계적가가만사,칙존재X상적가역유계선성혹자공액선성산자U화V사득등T∈B( X),유φ( T)=UTV。
Let B( X) be the Banach algebra of all bounded linear operators on an infinite dimensional complex Banach space X.We consider additive surjective maps preserving operators range or kernel inclusion in both directions.It is proved that ifφis an additive surjective map on B( X) preserving operators range or kernel inclusion in both directions, then there exist invertible bounded linear or conjugate linear operators U and V on X such that for every T∈B(X),φ( T)=UTV.