A Really Simple Elementary Proof of the Uniform Boundedness Principle in <i>F</i> -Spaces-Reference-Cited by-同舟云学术

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A Really Simple Elementary Proof of the Uniform Boundedness Principle in F -Spaces

Published:2024-06-18 Issue:0 Volume:0 Page:
ISSN:2391-4238
Container-title:Annales Mathematicae Silesianae
language:en
Short-container-title:

Author:

Ansorena José L.¹^ORCID

Affiliation:

1. Department of Mathematics and Computer Sciences , Universidad de La Rioja , Logroño Spain

Abstract

Abstract We give a proof of the uniform boundedness principle for linear continuous maps from F -spaces into topological vector spaces which is elementary and also quite simple.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/amsil-2024-0017

Reference5 articles.

1. S. Banach and H. Steinhaus, Sur le principe de la condensation de singularités, Fund. Math. 9 (1927), 50–60.

2. N.J. Kalton, N.T. Peck, and J.W. Roberts, An F -space Sampler, London Math. Soc. Lecture Note Ser., 89, Cambridge University Press, Cambridge, 1984.

3. W. Rudin, Functional Analysis, Second ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, Inc., New York, 1991.

4. A.D. Sokal, A really simple elementary proof of the uniform boundedness theorem, Amer. Math. Monthly 118 (2011), no. 5, 450–452.

5. C. Swartz, The evolution of the uniform boundedness principle, Math. Chronicle 19 (1990), 1–18.

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