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

Volume 8, Issue 5, pp 540--556
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### 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.

### 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.

•  46A30
•  46A16
•  46S50

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