一类算子的换位代数的K-群

The K-groups of commutant algebras of a class of operators

令H是一个复的、可分的、无穷维的Hilbert空间,L(H)表示H上有界线性算子的全体.算子T∈L(H)称为强不可约的,如果的换位代数没有非平凡的幂等元.本文对于算子类F={T∈L(H)<σ(T)连通,且A'(T)={R(T)<R为σ(T)上的解析函数}进行了研究,对于T∈F,证明了T是强不可约算子,且V(A'(T))=N,K_0(A'(T))=Z,这里N={0,1,2,3,...},Z是整数群.

Let H be a complex, separable, infinite dimensional Hilbert space and L（H） denote the collection of bounded linear operators on H. An operator T in L（H）is said to be strongly irreducible, if A＇（T） has no non-trivial idempotent.In the paper, we discuss the following operator class： F={T∈L（H）σ（T）= is connected and A＇（T）={R（T）R is the holomorphic function in σ（T）}. For T∈F,we prove that T is a stongly irreducible operator and V（A＇（T））=N,K_0（A＇（T））=Z,0,where N= {0, 1, 2, 3,...}, Z is integer group.