On the Banach-Steinhaus Theorem and the Continuity of Bilinear Mappings

Ronald Beattie; H.-P. Butzmann

doi:10.1002/mana.19911530126

On the Banach-Steinhaus Theorem and the Continuity of Bilinear Mappings

Mathematische Nachrichten ◽

10.1002/mana.19911530126 ◽

1991 ◽

Vol 153 (1) ◽

pp. 297-312 ◽

Cited By ~ 3

Author(s):

Ronald Beattie ◽

H.-P. Butzmann

Keyword(s):

Steinhaus Theorem

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A Note on the Banach-Steinhaus Theorem

Real Analysis Exchange ◽

10.2307/44152218 ◽

1991 ◽

Vol 17 (1) ◽

pp. 399 ◽

Cited By ~ 1

Author(s):

Olevskii

Keyword(s):

Steinhaus Theorem

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The Banach-Steinhaus Theorem with Rates, and Applications to Various Branches of Analysis

General Inequalities 2 - International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique ◽

10.1007/978-3-0348-6324-7_27 ◽

1980 ◽

pp. 299-331 ◽

Cited By ~ 8

Author(s):

P. L. Butzer

Keyword(s):

Steinhaus Theorem

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Barrelled Linearly Topologized Modules Over a Discrete Valuation Ring

Journal of Mathematics Research ◽

10.5539/jmr.v12n1p69 ◽

2020 ◽

Vol 12 (1) ◽

pp. 69

Author(s):

Dinamérico P. Pombo Jr ◽

Patricia Couto G. Mauro

Keyword(s):

Valuation Ring ◽

Discrete Valuation Ring ◽

Continuous Linear ◽

Steinhaus Theorem

In this paper barrelled linearly topologized modules over an arbitrary discrete valuation ring are introduced. A general form of the Banach-Steinhaus theorem for continuous linear mappings on barrelled linearly topologized modules is established and some consequences of it are derived.

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