Representing and absolutely representing systems
Kadets, V. ; Korobeĭnik, Yu.
Studia Mathematica, Tome 103 (1992), p. 217-223 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:215924
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Kadets, V.; Korobeĭnik, Yu. Representing and absolutely representing systems. Studia Mathematica, Tome 103 (1992) pp. 217-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i3p217bwm/

[00000] [1] E. Dubinsky, The Structure of Nuclear Fréchet Spaces, Lecture Notes in Math. 720, Springer, 1979. | Zbl 0403.46005

[00001] [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).

[00002] [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.

[00003] [4] Yu. F. Korobeĭnik, Representing systems, Uspekhi Mat. Nauk 36 (1) (1981), 73-126; English transl.: Russian Math. Surveys 36 (1) (1981), 75-137.

[00004] [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).

[00005] [6] A. Pietsch, Nukleare lokalkonvexe Räume, Akademie-Verlag, Berlin 1965. | Zbl 0152.32302

[00006] [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).