Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (5): 1071-1082.

• Articles • Previous Articles     Next Articles

Resonance Theorems for Families of Pointwise Semi-bounded and Non-unbounded Linear Operators on F* Spaces

 SONG Ming-Liang   

  1. Mathematics and Information Technology School, Jiangsu Second Normal University, Nanjing 210013
  • Received:2013-10-09 Revised:2014-08-04 Online:2014-10-25 Published:2014-10-25
  • Supported by:

    国家自然科学基金(10671094)、江苏省高校“青蓝工程”基金(2010QLP27)和江苏省高校自然科学基金(13KJB110004)资助.

Abstract:

We prove that every F* space (i.e., Hausdorff topological vector space satisfying the first countable axiom) can be characterized by meams of its “standard generating family of pseudo-norms”. By using the standard generating family of pseudo-norms P, the concepts of P-bounded set, P-semi-bounded set and P-unbounded set in F* space are introduced. The resonance theorems for families of pointwise semi-bounded and pointwise non-unbounded linear operators on F* spaces are established. As their applications, the resonance theorems for families of pointwise probabilistically semi-bounded  and pointwise probabilistically non-unbounded linear operators in Menger probabilistic normed spaces are obtained.

Key words: F* space, P-bounded set,  P-semi-bounded set,  P-unbounde set, Resonance theorem

CLC Number: 

  • 46A16
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