K-THEORY FOR FRÉCHET ALGEBRAS
K-THEORY FOR FRÉCHET ALGEBRAS
复制标题
弗雷谢代数的 K 理论
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
N. Phillips
中科院分区：
文献类型：
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作者：
N. Phillips
本文定义了Frechet代数的K-理论（假设是局部乘凸的），从而同时推广了σ-C*-代数的K-理论和Banach代数的K-理论.关于σ-C*-代数的K-理论的主要结果类似于关于空间的可表示K-理论的标准定理，可以推广到更一般的情况。我们的理论在另外两种情况下也给出了预期的结果。若Frechet代数的可逆元是开集，如全纯泛函演算下闭的C*-代数的稠密子代数，则我们的理论与应用Banach代数定义的结果一致.对于交换单位Frechet代数，我们的K-理论与具有紧生成拓扑的极大理想空间的可表示K-理论是相同的。
We define K-theory for Frechet algebras (assumed to be locally multiplicatively convex) so as to simultaneously generalize K-theory for σ-C*-algebras and K-theory for Banach algebras. The main results on K-theory of σ-C*-algebras, which are analogs of standard theorems on representable K-theory of spaces, carry over to the more general case. Our theory also gives the expected results in two other cases. If the invertible elements of a Frechet algebra are an open set, as is the case for dense subalgebras of C*-algebras closed under holomorphic functional calculus, then our theory agrees with the result of applying the Banach algebra definition. For commutative unital Frechet algebras, our K-theory is the same as the representable K-theory of the maximal ideal space with its compactly generated topology.