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 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |