On the uniform boundedness theorem in fuzzy quasi-normed spaces

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• 作者：Carmen Alegre ; ¹ ; ^{calegre@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Salvador Romaguera¹ ; ^{sromague@mat.upv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fuzzy quasi-norm ; Fuzzy norm ; Uniformly fuzzy bounded ; Equicontinuous ; Quasi-normed space ; Paratopological vector space
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：282
• 期：Complete
• 页码：143-153
• 全文大小：321 K

文摘

We prove that a family of continuous linear operators from a fuzzy quasi-normed space of the half second category to a fuzzy quasi-normed space is uniformly fuzzy bounded if and only if it is pointwise fuzzy bounded. This result generalizes and unifies several well-known results; in fact, the classical uniform boundedness principle, or Banach–Steinhauss theorem, is deduced as a particular case. Furthermore, we establish the relationship between uniform fuzzy boundedness and equicontinuity which allows us to give a uniform boundedness theorem in the class of paratopological vector spaces. The classical result for topological vector spaces is deduced as a corollary.