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 Vladikavkaz. Mat. Zh., 2010, Volume 12, Number 3, Pages 47–55 (Mi vmj183)

Some topics of the theory of linear topological spaces (completeness, non-trivial expansions of zero and their generators)

Yu. F. Korobeinikab

a Southern Federal University, Russia, Rostov-on-Don
b South Mathematical Institute of VSC RAS

Abstract: The connection between the existence of non-trivial expansions of zero with respect to some system of elements in a separated linear topological space and the completeness of such systems is investigated. The notion of a generator of non-trivial expansions of zero with respect to the system $X$ is introduced and some sufficient conditions under which the element $x$ generates non-trivial expansions of zero with respect to certain systems of elements are found.

Key words: complete system of elements in topological vector space, nontrivial expansions of zero.

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UDC: 517.9

Citation: Yu. F. Korobeinik, “Some topics of the theory of linear topological spaces (completeness, non-trivial expansions of zero and their generators)”, Vladikavkaz. Mat. Zh., 12:3 (2010), 47–55

Citation in format AMSBIB
\Bibitem{Kor10} \by Yu.~F.~Korobeinik \paper Some topics of the theory of linear topological spaces (completeness, non-trivial expansions of zero and their generators) \jour Vladikavkaz. Mat. Zh. \yr 2010 \vol 12 \issue 3 \pages 47--55 \mathnet{http://mi.mathnet.ru/vmj183} \elib{http://elibrary.ru/item.asp?id=15181020}