Displaying similar documents to “The uniform boundedness principle for order bounded operators.”

A uniform boundedness principle of Pták

Charles W. Swartz (1993)

Commentationes Mathematicae Universitatis Carolinae

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The Antosik-Mikusinski Matrix Theorem is used to give an extension of a uniform boundedness principle due to V. Pták to certain metric linear spaces. An application to bilinear operators is given.

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu

Francy Armao, Dorota Głazowska, Sergio Rivas, Jessica Rojas (2013)

Open Mathematics

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We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.

Uniform maps into normed spaces

Zdeněk Frolìk (1974)

Annales de l'institut Fourier

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Thirteen properties of uniform spaces are shown to be equivalent. The most important properties seem to be those related to modules of uniformly continuous mappings into normed spaces, and to partitions of unity.