On prequojections and their duals.

M. I. Ostrovskii

Revista Matemática Complutense (1998)

  • Volume: 11, Issue: 1, page 59-77
  • ISSN: 1139-1138

Abstract

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The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce a special class of prequojections, we call them canonical, and show that in the main result of G. Metafune and V. B. Moscatelli on the existence of a prequojection with a given dual we may require this prequojection to be a canonical one.

How to cite

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Ostrovskii, M. I.. "On prequojections and their duals.." Revista Matemática Complutense 11.1 (1998): 59-77. <http://eudml.org/doc/44482>.

@article{Ostrovskii1998,
abstract = {The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce a special class of prequojections, we call them canonical, and show that in the main result of G. Metafune and V. B. Moscatelli on the existence of a prequojection with a given dual we may require this prequojection to be a canonical one.},
author = {Ostrovskii, M. I.},
journal = {Revista Matemática Complutense},
keywords = {Espacios lineales topológicos; Espacios de Frechet; Análisis canónico; Espacio dual; Fréchet spaces; prequojections},
language = {eng},
number = {1},
pages = {59-77},
title = {On prequojections and their duals.},
url = {http://eudml.org/doc/44482},
volume = {11},
year = {1998},
}

TY - JOUR
AU - Ostrovskii, M. I.
TI - On prequojections and their duals.
JO - Revista Matemática Complutense
PY - 1998
VL - 11
IS - 1
SP - 59
EP - 77
AB - The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce a special class of prequojections, we call them canonical, and show that in the main result of G. Metafune and V. B. Moscatelli on the existence of a prequojection with a given dual we may require this prequojection to be a canonical one.
LA - eng
KW - Espacios lineales topológicos; Espacios de Frechet; Análisis canónico; Espacio dual; Fréchet spaces; prequojections
UR - http://eudml.org/doc/44482
ER -

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