Geodesic
A rigid space admitting compact operators
Studia Mathematica, Tome 112 (1994) no. 3, pp. 213-228
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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. 
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Paul Sisson. A rigid space admitting compact operators. Studia Mathematica, Tome 112 (1994) no. 3, pp. 213-228. doi: 10.4064/sm-112-3-213-228

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