# A rigid space admitting compact operators

Studia Mathematica (1995)

- Volume: 112, Issue: 3, page 213-228
- ISSN: 0039-3223

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topSisson, Paul. "A rigid space admitting compact operators." Studia Mathematica 112.3 (1995): 213-228. <http://eudml.org/doc/216149>.

@article{Sisson1995,

abstract = {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.},

author = {Sisson, Paul},

journal = {Studia Mathematica},

keywords = {rigid space admitting compact operators},

language = {eng},

number = {3},

pages = {213-228},

title = {A rigid space admitting compact operators},

url = {http://eudml.org/doc/216149},

volume = {112},

year = {1995},

}

TY - JOUR

AU - Sisson, Paul

TI - A rigid space admitting compact operators

JO - Studia Mathematica

PY - 1995

VL - 112

IS - 3

SP - 213

EP - 228

AB - 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.

LA - eng

KW - rigid space admitting compact operators

UR - http://eudml.org/doc/216149

ER -

## References

top- [1] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-Space Sampler, Cambridge Univ. Press, Cambridge, 1984.
- [2] N. J. Kalton and J. W. Roberts, A rigid subspace of ${L}_{0}$, Trans. Amer. Math. Soc. 266 (1981), 645-654. Zbl0484.46004
- [3] N. J. Kalton and J. H. Shapiro, An F-space with trivial dual and non-trivial compact endomorphisms, Israel J. Math. 20 (1975), 282-291. Zbl0305.46008
- [4] D. Pallaschke, The compact endomorphisms of the metric linear spaces ${\mathcal{L}}_{\phi}$, Studia Math. 47 (1973), 123-133. Zbl0256.46030
- [5] P. D. Sisson, Compact operators on trivial-dual spaces, PhD thesis, Univ. of South Carolina, Columbia, South Carolina, 1993.
- [6] P. Turpin, Opérateurs linéaires entre espaces d'Orlicz non localement convexes, Studia Math. 46 (1973), 153-165. Zbl0254.46022
- [7] L. Waelbroeck, A rigid topological vector space, ibid. 59 (1977), 227-234. Zbl0344.46008

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