交换Herm itian Banach~*-代数的稳定秩

The Stable Rank of Commutative Hermitian Banach~*-Algebras

设 A是有单位元的交换 Hermitian Banach* -代数 ,MA 是 A的谱空间。则tsr( A) =dim MA2 + 1 ,csr( A) 1 + dim MA2 + 1。由此 ,当 A是 Wiener环或是 Sobolev空间 Wm,p ( Ω) (其中 ,2 <mp 2 + p,Ω是 C中具有强局部Lipschitz性质的区域 ) ,得到了 tsr( A)及 csr( A)

Let A be a unital commutative Hermitian Banach* algebra and M A be its spetral space. Then tsr( A )=dim M A2+1,csr A 1+dim M A2+1. So if A is the Wiener ring or the Sobolev space W m,p (Ω )(where 2< mp<p +2, Ω is the domain in C with strongly local Lipechitz property), the value of tsr ( A ) and csr ( A ) is obtained.