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The uniform boundedness theorem in b-Banach space

Volume 6, Issue 2, April 2021    |    PP. 25-32    |PDF (192 K)|    Pub. Date: May 17, 2021
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Author(s)
Jiachen Lv, School of Science, Wuhan University of Science and Technology, Wuhan, China
Yuqiang Feng, School of Science, Wuhan University of Science and Technology, Wuhan, China

Abstract
B-Banach space is an extension of Banach space, which provides a suitable framework for studying many analytical problems. The uniform boundedness theorem is is the basic theorem in functional analysis and has many important applications in many field, such as matrix analysis, operator theory, and numerical analysis. In this note, we revisit the concept of b-Banach space, and then establish the uniform boundedness theorem for linear operators. The result may be useful to establish linear operator theory in b-Banach space.

Keywords
B-normed linear space, B-Banach space, Uniform boundedness theorem

Cite this paper
Jiachen Lv, Yuqiang Feng, The uniform boundedness theorem in b-Banach space, SCIREA Journal of Mathematics. Vol. 6 , No. 2 , 2021 , pp. 25 - 32 .

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