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Counterexample to a problem of Geoghegan-West

Authors:	P V Semenov

Institution:	1614. app149, Zelenograd, Moscow, 103617, Russia

Abstract:	Let be a Banach space and $\mathrm{GL}(X)$ its general linear group. Let $\\|\cdot\\|$ denote the operator norm and ``' the pointwise convergence topology on $\mathrm{GL}(X)$ . Is the identity map $(\mathrm{GL}(X),\\|\cdot\\|)\rightarrow(\mathrm{GL}(X),w)$ a homotopy equivalence? The answer is negative. One of the possible counterexamples is a well-known James space $\mathbb J$ ---the ``space of counterexamples in Banach spaces theory'.

Keywords:	General linear group pointwise convergence topology weak homotopy equivalence James space

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