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 Trudy Mat. Inst. Steklova, 2005, Volume 248, Pages 130–143 (Mi tm126)

Almost Normed and Quasinormed Spaces

L. D. Kudryavtsev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The properties of various classes of almost normed spaces and the spaces of their bounded linear operators are studied. It is shown that these spaces of operators are Banach spaces under certain conditions. It is proved that a bounded linear operator can be extended, while preserving its norm, from a dense set in an almost normed space to the entire space.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 248, 125–137

Bibliographic databases:
UDC: 517.982

Citation: L. D. Kudryavtsev, “Almost Normed and Quasinormed Spaces”, Studies on function theory and differential equations, Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 248, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 130–143; Proc. Steklov Inst. Math., 248 (2005), 125–137

Citation in format AMSBIB
\Bibitem{Kud05} \by L.~D.~Kudryavtsev \paper Almost Normed and Quasinormed Spaces \inbook Studies on function theory and differential equations \bookinfo Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii \serial Trudy Mat. Inst. Steklova \yr 2005 \vol 248 \pages 130--143 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm126} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2165923} \zmath{https://zbmath.org/?q=an:1128.46011} \transl \jour Proc. Steklov Inst. Math. \yr 2005 \vol 248 \pages 125--137