The Stable Rank of Topological Algebras and a Problem of R.G. Swan

1998/06/26 by C. Badea, Badea, C.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.math/9806145

AMS-LaTeX, 29 pages, submitted to J. Funct. Anal

arxiv created 1998/06/26 · arxiv updated 2009/11/30

Abstract

Various notions of stable ranks are studied for topological algebras. Some partial answers to R.G. Swan's problem (Have two Banach or good Fréchet algebras as in the density theorem in K-theory the same stable rank ?) are obtained. For example, a Fréchet dense ∗-subalgebra A of a C^∗-algebra B, closed under C^∞-functional calculus of self-adjoint elements, has the same Bass stable rank as B.

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