Representing and absolutely representing systems

• Autorzy: V. M. Kadets , Yu. F. Korobeĭnik
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A35: Summability and bases
• 46A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 102
• Numer: 3
• Strony: 217-223

Daty

wydano

1992

otrzymano

1991-03-28

poprawiono

1991-10-18

Twórcy

autor

V. M. Kadets

• Departament of Mathematics, Kharkov State University, 310000 Kharkov, Ukraine

autor

Yu. F. Korobeĭnik

• Department of Mathematics, Rostov State University, 344711 Rostov-Na-Donu, Russia

Bibliografia

• [1] E. Dubinsky, The Structure of Nuclear Fréchet Spaces, Lecture Notes in Math. 720, Springer, 1979.
• [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] 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] Yu. F. Korobeĭnik, Representing systems, Uspekhi Mat. Nauk 36 (1) (1981), 73-126; English transl.: Russian Math. Surveys 36 (1) (1981), 75-137.
• [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] A. Pietsch, Nukleare lokalkonvexe Räume, Akademie-Verlag, Berlin 1965.
• [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).