Relatively spectral morphisms and applications to K-theory

Details Relatively spectral morphisms and applications to K-theory Relatively spectral morphisms and applications to K-theory

2008-05-30

arxiv.org/abs/0805.4788v2

Journal of Functional Analysis 255 (2008), 3303 - 3328

Mathematics

Operator Algebras

21 pages, final version

Scientific paper

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.

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