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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2013, Volume 9, Number 4, Pages 448–454
(Mi jmag575)
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A Remark on Condensation of Singularities
J.-D. Hardtke Department of Mathematics Freie Universität Berlin,
Arnimallee 6, Berlin 14195, Germany
Abstract:
Recently Alan D. Sokal in Amer. Math. Monthly 118 (2011), No. 5, 450–452, gave a very short and completely elementary proof of the uniform boundedness principle. The aim of this note is to point out that by using a similar technique one can give a short and simple proof of a stronger statement, namely a principle of condensation of singularities for certain double-sequences of non-linear operators on quasi-Banach spaces, which is a bit more general than a result of I. S. Gál from Duke Math. J. 20 (1953), No. 1, 27–35.
Key words and phrases:
uniform boundedness principle, principle of condensation of singularities, quasi-Banach spaces, non-linear operators.
Received: 13.11.2012
Citation:
J.-D. Hardtke, “A Remark on Condensation of Singularities”, Zh. Mat. Fiz. Anal. Geom., 9:4 (2013), 448–454
Linking options:
https://www.mathnet.ru/eng/jmag575 https://www.mathnet.ru/eng/jmag/v9/i4/p448
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Abstract page: | 148 | Full-text PDF : | 85 | References: | 35 |
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