Banach spaces without the Kadec $H$-property (solution of a problem from the ``Scottish Book'') |
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| Author |
Institute of Applied Problems of Mechanics and Mathematics,National Academy of Sciences, Naukova 3b, 290053 L'viv, Ukraine.
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| Abstract |
It is proved that if a separable Banach space $X$ has not the
Schur property then there exists an equivalent strictly convex
norm on $X$ without $H$-property.
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| Keywords |
separable Banach space, Schur property, strictly convex norm, H-property
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| DOI |
doi:10.30970/ms.7.1.59-60
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Reference |
1. . Кадець М.Й. Про зв'язок мiж слабою та сильною збiжнiстю // Доповiдi АН УРСР – 1959 p. №9, С.949–952
2. Mauldin R. D. (ed.) The Scottish Book. , Boston e.a.: Birkhä.user– 1981 3. Singer I. Bases in Banach spaces II. , Bucuresti - Berlin e.a.: Editura Academiei - Springer– 1981 4. Radon J. Theorie und Anwendungen der absolut additiven Mengenfunktionen // Sitzungsberichte der Acad. für Wissensch. in Wien– 1913 Abs. II-a, V. 122 p. S.1295–1438 5. Riesz F. Sur la convergence en moyenne // Acta Sci. Math. Szeged – 1928–1929. V. 4 p. I – P.58–64; II – P.182–185 |
| Pages |
59-60
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| Volume |
7
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| Issue |
1
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| Year |
1997
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| Journal |
Matematychni Studii
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