ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 14 (2019), 219 -- 229
This work is licensed under a Creative Commons Attribution 4.0 International License.
THE FUNDAMENTAL AND WEAKLY CONTINUOUS PROPERTIES IN COMPLEMENTED TOPOLOGICAL ALGEBRAS
Marina Haralampidou and Konstantinos Tzironis
Abstract. We give conditions so that a certain left complemented algebra turns to be a fundamental one. In the case when the only minimal closed right ideals of a certain complemented algebra (E, ⊥) are axial, namely they have the form eE with e a special element and its vector complementor is continuous, then ⊥ is weakly continuous. Moreover, conditions are supplied so that a left precomplemented locally m-convex algebra turns to be a complemented one.
2010 Mathematics Subject Classification: 46H05; 46H10; 46A03.
Keywords: Complemented vector space; left complemented algebra; topologically simple algebra; fundamental topological linear space; fundamental topological algebra; axially closed element; (weakly) continuous complementor.
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Marina Haralampidou
Department of Mathematics,
National and Kapodistrian University of Athens,
Panepistimioupolis, Athens 15784, Greece
e-mail: mharalam@math.uoa.gr
Konstantinos Tzironis
Department of Mathematics,
National and Kapodistrian University of Athens,
Panepistimioupolis, Athens 15784, Greece
e-mail: tzirk@math.uoa.gr