A rigid space admitting compact operators

Paul Sisson

Studia Mathematica (1995)

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

Abstract

top
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.

How to cite

top

Sisson, 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. [1] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-Space Sampler, Cambridge Univ. Press, Cambridge, 1984. 
  2. [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. [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. [4] D. Pallaschke, The compact endomorphisms of the metric linear spaces ℒ φ , Studia Math. 47 (1973), 123-133. Zbl0256.46030
  5. [5] P. D. Sisson, Compact operators on trivial-dual spaces, PhD thesis, Univ. of South Carolina, Columbia, South Carolina, 1993. 
  6. [6] P. Turpin, Opérateurs linéaires entre espaces d'Orlicz non localement convexes, Studia Math. 46 (1973), 153-165. Zbl0254.46022
  7. [7] L. Waelbroeck, A rigid topological vector space, ibid. 59 (1977), 227-234. Zbl0344.46008

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.