$\infty$-Convex sets and their applications to the proof of certain classical theorems of functional analysis |
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| Author |
wlanc@litech.lviv.ua
Department of Mathematics, Lviv University,Universytetska 1, Lviv, 290602,
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| Abstract |
Using the notion of an $\infty$-convex set we present a
new geometric proof of two classical theorems of functional analysis:
Banach Open Mapping Principle and Banach-Mazur Theorem on quotients of
$l_1$.
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| Keywords |
Banach Open Mapping Principle, Banach-Mazur theorem, functional analysis, convexity in Banach spaces
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| DOI |
doi:10.30970/ms.11.1.83-84
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Reference |
1. S. Banach Theorie des operations lineaires,addr Warszawa, PWN–1932
2. S. Banach, S. Mazur Zur Theorie der linearen Dimension// Studia Math.V. 4–1933p.100–112 |
| Pages |
83-84
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| Volume |
11
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| Issue |
1
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| Year |
1999
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| Journal |
Matematychni Studii
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| Full text of paper | |
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