1Department of Mathematics, H. H. The Rajah's College 2Department of Mathematics, Alagappa University, Karaikudi - 630 005,
Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 317-320
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C. T. Ramasamy; C. Ganesa Moorthy; C. T. Ramasamy; C. Ganesa Moorthy. Uniform boundedness Principle for unbounded Operators. Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 317-320. http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a13/
@article{AMUC_2014_83_2_a13,
author = {C. T. Ramasamy and C. Ganesa Moorthy and C. T. Ramasamy and C. Ganesa Moorthy},
title = { Uniform boundedness {Principle} for unbounded {Operators}},
journal = {Acta mathematica Universitatis Comenianae},
pages = {317--320},
year = {2014},
volume = {83},
number = {2},
url = {http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a13/}
}
TY - JOUR
AU - C. T. Ramasamy
AU - C. Ganesa Moorthy
AU - C. T. Ramasamy
AU - C. Ganesa Moorthy
TI - Uniform boundedness Principle for unbounded Operators
JO - Acta mathematica Universitatis Comenianae
PY - 2014
SP - 317
EP - 320
VL - 83
IS - 2
UR - http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a13/
ID - AMUC_2014_83_2_a13
ER -
%0 Journal Article
%A C. T. Ramasamy
%A C. Ganesa Moorthy
%A C. T. Ramasamy
%A C. Ganesa Moorthy
%T Uniform boundedness Principle for unbounded Operators
%J Acta mathematica Universitatis Comenianae
%D 2014
%P 317-320
%V 83
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a13/
%F AMUC_2014_83_2_a13
A uniform boundedness principle for unbounded operators is derived. A particular case is: Suppose $\{T\}_{i\in I}$ be a family of linear mappings of a Banach space $X$ into a normed space $Y$ such that $\{T_ix : i \in I\}$ is bounded for each $x \in X$;then there exists a dense subset $A$ of the open unit ball in $X$ such that $\{T_ix : i \in I, x\in A\}$ is bounded. A closed graph theorem and a bounded inverse theorem are obtained for families of linear mappings as consequences of this principle. Someapplications of this principle are also obtained.
