A rigid space admitting compact operators

• Autorzy: Paul Sisson
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54G15: Pathological spaces
• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994-1995
• Tom: 112
• Numer: 3
• Strony: 213-228

Daty

wydano

1995

otrzymano

1993-09-13

Twórcy

autor

Paul Sisson

• Department of Mathematics, Louisiana State University-Shreveport, Shreveport, Louisiana 71115 U.S.A.

Bibliografia

• [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.
• [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.
• [4] D. Pallaschke, The compact endomorphisms of the metric linear spaces $ℒ_φ$, Studia Math. 47 (1973), 123-133.
• [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.
• [7] L. Waelbroeck, A rigid topological vector space, ibid. 59 (1977), 227-234.