The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces


Authors

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.


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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


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