Mathematics – Operator Algebras
Scientific paper
1998-06-26
Mathematics
Operator Algebras
AMS-LaTeX, 29 pages, submitted to J. Funct. Anal
Scientific paper
Various notions of stable ranks are studied for topological algebras. Some partial answers to R.G. Swan's problem (Have two Banach or good Fr\'echet algebras as in the density theorem in K-theory the same stable rank ?) are obtained. For example, a Fr\'echet dense $\ast$-subalgebra $A$ of a $C^\ast$-algebra $B$, closed under $C^\infty$-functional calculus of self-adjoint elements, has the same Bass stable rank as $B$.
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