Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 1 -- 27

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REPRESENTATIONS OF (QUASI-)COMPLEMENTED ALGEBRAS

Marina Haralampidou and Konstantinos Tzironis

Abstract. We deal with (pre-Hilbert and or Hilbert space) representations of algebraic structu-res equipped with compatible topologies. Among them we explore the representation theory in the context of certain left (quasi-)complemented (non-normed) topological algebras. To face this problem, we apply either the Kakutani-Mackey-like theorem (a kind of a partial (non-normed) generalization of a classical Kakutani-Mackey theorem) or the Arens-Michael decomposition.

2020 Mathematics Subject Classification: 46H15; 22A30; 46K10.
Keywords: Quasi-complemented vector space; left (quasi-) complemented algebra; topologically simple algebra; automorphically perfect pair; Arens--Michael decomposition.

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Marina Haralampidou
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece.
e-mail: mharalam@math.uoa.gr
Konstantinos Tzironis
Department of Mathematics, University of Athens, Panepistimioupolis, Athens 15784, Greece.
e-mail: tzirk@math.uoa.gr

http://www.utgjiu.ro/math/sma