Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
Keyword(s):
AbstractWe prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinitedimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X whose set of zeros is F, and X/F is infinite-dimensional, then X and X \ F are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and the n-torus on certain Banach spaces.
2005 ◽
Vol 72
(2)
◽
pp. 299-315
◽
2001 ◽
Vol 33
(4)
◽
pp. 443-453
◽
1988 ◽
Vol 103
(3)
◽
pp. 497-502
2011 ◽
Vol 53
(3)
◽
pp. 443-449
◽