A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid spaces was demonstrated.
@article{bwmeta1.element.bwnjournal-article-smv112i3p213bwm,
author = {Paul Sisson},
title = {A rigid space admitting compact operators},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {213-228},
zbl = {0834.46005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv112i3p213bwm}
}
Sisson, Paul. A rigid space admitting compact operators. Studia Mathematica, Tome 113 (1995) pp. 213-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i3p213bwm/
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