K-理论在一类算子逼近中的应用

K-theory and Approximation of a Class of Operators

构造了一类强不可约的Cowen—Douglas算子,刻画了其换位代数的K_0-群.我们证明了:对于复可分的Hilbert空间上的有界线性算子T及ε>0,总可以找到由有限多个强不可约的Cowen-Douglas算子构成的直和算子S,使得||T-S||<ε.

We construct a class of strongly irreducible Cowen-Douglas operators and characterize the K_0-groups of their commutant algebras.Then we show that for each bounded linear operator T on a complex separable Hilbert space and ε〉 0,there exists an operator S which can be written as a direct sum of finitely many strongly irreducible Cowen-Douglas operators with nice properties such that ｜｜T — S｜｜〈 ε.