ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




Uniform Boundedness principle for unbounded operators

C. Ganesa Moorthy and CT. Ramasamy

Received: November 7, 2013;   Accepted: February 17, 2014



Abstract.   A uniform boundedness principle for unbounded operators is derived. A particular case is: Suppose {Ti}i in I be a family of linear mappings of a Banach space X into a normed space Y such that {Tix : i in I} is bounded for each x in X; then there exists a dense subset A of the open unit ball in X such that {Tix : i in I, x in A} is bounded. A closed graph theorem and a bounded inverse theorem are obtained for families of linear mappings as consequences of this principle. Some applications of this principle are also obtained.


Keywords:  Uniform boundedness principle; closed graph theorem.  

AMS Subject classification: Primary:  46A32, 47L60  


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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