Spaces of sections of Banach algebra bundles

作者：Farjoun Emmanuel Dror^*; Schochet Claude L

来源：Journal of K-Theory, 2012, 10(2): 279-298.

DOI：10.1017/is012002001jkt183

• general linear group of a Banach algebra
• spectral sequences
• localization
• Bott-stable
• K-theory for Banach algebras
• unstable K-theory

Suppose that B is a G-Banach algebra over F = R or C, X is a finite dimensional compact metric space, zeta : P -%26gt; X is a standard principal G-bundle, and A(zeta) = Gamma(X, P x(G) B) is the associated algebra of sections. We produce a spectral sequence which converges to pi(*)(GL(o)A(zeta)) with %26lt;br%26gt;E--p,q(2) congruent to H-p(X; pi(q)(GL(o)B)). %26lt;br%26gt;A related spectral sequence converging to K*+1(A(zeta)) (the real or complex topological K-theory) allows us to conclude that if B is Bott-stable, (i.e., if pi(*)(GL(o)B) -%26gt; K*+1(B) is an isomorphism for all * %26gt; 0) then so is A(zeta).

• 出版日期2012-10