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Zh. Mat. Fiz. Anal. Geom., 2013, Volume 9, Number 4, Pages 448–454 (Mi jmag575)  

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.

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Bibliographic databases:
MSC: 46A16, 47H99
Received: 13.11.2012
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Citation: J.-D. Hardtke, “A Remark on Condensation of Singularities”, Zh. Mat. Fiz. Anal. Geom., 9:4 (2013), 448–454

Citation in format AMSBIB
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\by J.-D.~Hardtke
\paper A Remark on Condensation of Singularities
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2013
\vol 9
\issue 4
\pages 448--454
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