Representing and absolutely representing systems

V. Kadets; Yu. Korobeĭnik

Studia Mathematica (1992)

  • Volume: 102, Issue: 3, page 217-223
  • ISSN: 0039-3223

Abstract

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We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.

How to cite

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Kadets, V., and Korobeĭnik, Yu.. "Representing and absolutely representing systems." Studia Mathematica 102.3 (1992): 217-223. <http://eudml.org/doc/215924>.

@article{Kadets1992,
abstract = {We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.},
author = {Kadets, V., Korobeĭnik, Yu.},
journal = {Studia Mathematica},
keywords = {representing systems},
language = {eng},
number = {3},
pages = {217-223},
title = {Representing and absolutely representing systems},
url = {http://eudml.org/doc/215924},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Kadets, V.
AU - Korobeĭnik, Yu.
TI - Representing and absolutely representing systems
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 3
SP - 217
EP - 223
AB - We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.
LA - eng
KW - representing systems
UR - http://eudml.org/doc/215924
ER -

References

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  1. [1] E. Dubinsky, The Structure of Nuclear Fréchet Spaces, Lecture Notes in Math. 720, Springer, 1979. Zbl0403.46005
  2. [2] V. M. Kadets and Yu. F. Korobeĭnik, Representing systems in linear topological spaces, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk 1985 (2), 16-18 (in Russian). 
  3. [3] Yu. F. Korobeĭnik, On a dual problem. I. General results. Applications to Fréchet spaces, Mat. Sb. 97 (2) (1975), 193-229; English transl.: Math. USSR-Sb. 26 (2) (1975), 181-212. 
  4. [4] Yu. F. Korobeĭnik, Representing systems, Uspekhi Mat. Nauk 36 (1) (1981), 73-126; English transl.: Russian Math. Surveys 36 (1) (1981), 75-137. 
  5. [5] Yu. F. Korobeĭnik, On some problems of the theory of representing systems, in: Theory of Functions and of Approximations, Izdat. Saratov. Univ., 1986, 25-31 (in Russian). 
  6. [6] A. Pietsch, Nukleare lokalkonvexe Räume, Akademie-Verlag, Berlin 1965. Zbl0152.32302
  7. [7] A. A. Talalyan, On the existence of null series with respect to some systems of functions, Mat. Zametki 5 (1) (1969), 3-12 (in Russian). 

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