NEAR-ALGEBRA和BANACH代数上的一个特征值定理

Eigenvalue Theorem on Near-Algebra and Banach Algebra

摘要: 在near-algebra或Banach代数中引入(p,q)-可加自映象f和正则可逆元的概念,得到一个值得注意的结果,即在一定条件下,对于定义在near-algebra或Banach代数X中(p,q)-可加自映象f,X中的任意正则可逆元都具有公共的特征值λ=2q/(1+q),p=q≠-1。

Abstract: Let a (p,q)-additive selfmap f on near-algebra or Banach algebra X satisfy f (e)=e and f (u)=ϕ(u) f (u-1)φ(u) whereϕ:X → X andφ:X → DES(X) be an automorphism and antiautomorphism respectively such that ϕ(u)=uφ(u-1)u for each invertible u of X. Then all of the normal invertibles of X have the common eigenvalue λ=2q/(1+q) if p=q≠-1.