Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591647 | Journal of Functional Analysis | 2008 | 26 Pages |
Abstract
Spectral morphisms between Banach algebras are useful for comparing their K-theory and their “noncommutative dimensions” as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral information is only known over a dense subalgebra. We investigate such relatively spectral morphisms. We prove a relative version of the Density Theorem regarding isomorphism in K-theory. We also solve Swan's problem for the connected stable rank, in fact for an entire hierarchy of higher connected stable ranks that we introduce.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory