Counterexample to a problem of Geoghegan-West

Semenov, P.

doi:10.1090/S0002-9939-96-03276-5

Counterexample to a problem of Geoghegan-West
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by P. V. Semenov PDF

Proc. Amer. Math. Soc. 124 (1996), 939-943 Request permission

Abstract:

Let $X$ be a Banach space and $\mathrm {GL}(X)$ its general linear group. Let $\|\cdot \|$ denote the operator norm and “$w$” 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”.

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