应用泛函分析学报
應用汎函分析學報
응용범함분석학보
ACTA ANALYSIS FUNCTIONALIS APPLICATA
2001年
3期
231-235
,共5页
谱半径%乘法映射%秩1算子
譜半徑%乘法映射%秩1算子
보반경%승법영사%질1산자
spectral radius%multiplicative map%rank one operator
设X和Y为无限维Banach空间,φ:B(X)→B(Y)是保持谱半径的满射,且秩为1算子,则φ具有形式φ(T)=ATA-1,这里A:X→Y或是线性拓扑同构映射或是线性拓扑同构映射的共轭.
設X和Y為無限維Banach空間,φ:B(X)→B(Y)是保持譜半徑的滿射,且秩為1算子,則φ具有形式φ(T)=ATA-1,這裏A:X→Y或是線性拓撲同構映射或是線性拓撲同構映射的共軛.
설X화Y위무한유Banach공간,φ:B(X)→B(Y)시보지보반경적만사,차질위1산자,칙φ구유형식φ(T)=ATA-1,저리A:X→Y혹시선성탁복동구영사혹시선성탁복동구영사적공액.
Let X and Y be infinite-dimensional Banach spaces. If φ: B(X) → B(Y) is a surjective
multiplicative map preserving the spectral radius of rank one operators, then φ is of the form φ (T) =
ATA-1. Where A: X → Y is either a linear topological isomorphism or a conjugate linear topological
isomorphism.
