The uniform boundedness principles for \(\gamma\)maxpseudonormsubadditive and quasihomogeneous operators in \(F^*\) spaces

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Authors
Mingliang Song
 Mathematics and Information Technology School, Jiangsu Second Normal University, Nanjing, 210013, P. R. China.
Abstract
In this paper, we prove that every \(F^*\) space (i.e., Hausdorff topological vector space satisfying the first
countable axiom) can be characterized by means of its “standard generating family of pseudonorms”. By
using the standard generating family of pseudonorms \(\mathcal{P}\), the concepts of \(\mathcal{P}\)bounded set and \(\gamma\)maxpseudo
normsubadditive operator in \(F^*\) space are introduced. The uniform boundedness principles for
family of \(\gamma\)maxpseudonormsubadditive and quasihomogeneous operators in \(F^*\) spaces are established.
As applications, we obtain the corresponding uniform boundedness principles in classical normed spaces and
Menger probabilistic normed spaces.
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ISRP Style
Mingliang Song, The uniform boundedness principles for \(\gamma\)maxpseudonormsubadditive and quasihomogeneous operators in \(F^*\) spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 540556
AMA Style
Song Mingliang, The uniform boundedness principles for \(\gamma\)maxpseudonormsubadditive and quasihomogeneous operators in \(F^*\) spaces. J. Nonlinear Sci. Appl. (2015); 8(5):540556
Chicago/Turabian Style
Song, Mingliang. "The uniform boundedness principles for \(\gamma\)maxpseudonormsubadditive and quasihomogeneous operators in \(F^*\) spaces." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 540556
Keywords
 Uniform boundedness principle
 \(\gamma\)maxpseudonormsubadditive operator
 quasihomogeneous operator
 second category
 \(F^*\) space.
MSC
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