Boundedness of linear maps

T. S. S. R. K. Rao

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 1, page 107-110
  • ISSN: 0010-2628

Abstract

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In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.

How to cite

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Rao, T. S. S. R. K.. "Boundedness of linear maps." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 107-110. <http://eudml.org/doc/248629>.

@article{Rao2000,
abstract = {In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.},
author = {Rao, T. S. S. R. K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {bounded linear maps; extreme points; barrelled spaces; bounded linear maps; extreme points; barrelled spaces},
language = {eng},
number = {1},
pages = {107-110},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Boundedness of linear maps},
url = {http://eudml.org/doc/248629},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Rao, T. S. S. R. K.
TI - Boundedness of linear maps
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 1
SP - 107
EP - 110
AB - In this short note we consider necessary and sufficient conditions on normed linear spaces, that ensure the boundedness of any linear map whose adjoint maps extreme points of the unit ball of the domain space to continuous linear functionals.
LA - eng
KW - bounded linear maps; extreme points; barrelled spaces; bounded linear maps; extreme points; barrelled spaces
UR - http://eudml.org/doc/248629
ER -

References

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  2. Diestel J., Sequences and series in Banach spaces, GTM 92, Springer, Berlin, 1984. MR0737004
  3. Fonf V.P., Weakly extremal properties of Banach spaces, Math. Notes 45 (1989), 488-494. (1989) Zbl0699.46010MR1019040
  4. Fonf V.P., On exposed and smooth points of convex bodies in Banach spaces, Bull. London Math. Soc. 28 (1996), 51-58. (1996) Zbl0879.46001MR1356826
  5. Harmand P., Werner D., Werner W., M -ideals in Banach spaces and Banach algebras, Springer LNM 1547, Berlin, 1993. Zbl0789.46011MR1238713
  6. Labuschagne L.E., Mascioni V., Linear maps between C * algebras whose adjoints preserve extreme points of the dual unit ball, Advances in Math. 138 (1998), 15-45. (1998) Zbl0944.46054MR1645056
  7. Rao T.S.S.R.K., On the extreme point intersection property, ``Function spaces, the second conference'', Ed. K. Jarosz, Lecture Notes in Pure and Appl. Math. 172, Marcel Dekker, 1995, pp.339-346. Zbl0868.46011MR1352241
  8. Wilansky A., Modern methods in topological vector spaces, McGraw Hill, New York, 1978. Zbl0395.46001MR0518316

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