The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces
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Ming-liang 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 pseudo-norms”. By
using the standard generating family of pseudo-norms \(\mathcal{P}\), the concepts of \(\mathcal{P}\)-bounded set and \(\gamma\)-maxpseudo-
norm-subadditive operator in \(F^*\) space are introduced. The uniform boundedness principles for
family of \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces are established.
As applications, we obtain the corresponding uniform boundedness principles in classical normed spaces and
Menger probabilistic normed spaces.
Share and Cite
ISRP Style
Ming-liang Song, The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 540--556
AMA Style
Song Ming-liang, The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces. J. Nonlinear Sci. Appl. (2015); 8(5):540--556
Chicago/Turabian Style
Song, Ming-liang. "The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 540--556
Keywords
- Uniform boundedness principle
- \(\gamma\)-max-pseudo-norm-subadditive operator
- quasi-homogeneous operator
- second category
- \(F^*\) space.
MSC
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