arXiv math/99060731999-06-11math.OA

Stable Ranks, K-Groups and Witt Groups of some Banach and C-star Algebras

C. Badea

备注：: 19 pages, to appear in Contemporary Math
发表信息：: Contemporary Math. (A.M.S.) 232(1999), 55-64.

英文摘要：

We show that certain dense and spectral invariant subalgebras of a $C^*$-algebra have the same bilateral Bass stable rank. This is a partial answer for (a version of) an open problem raised by R.G. Swan. Then, for certain Banach algebras, we indicate when the homotopy groups $π_{i}(GL_{n}(A))$ stabilize for large $n$. This is an improvement of a result due to G. Corach and A. Larotonda. Using some results due to M. Karoubi, we show the isomorphism of the Witt group of a symmetric Banach algebra with the $K_0$-group of its enveloping $C^*$-algebra. The question if this is true for all involutive Banach algebras was raised by A. Connes.

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