Advances in Operator Theory

A Kakutani–Mackey-like theorem

Marina Haralampidou and Konstantinos Tzironis

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Abstract

We give a partial extension of a Kakutani–Mackey theorem for quasi-complemented vector spaces. This can be applied in the representation theory of certain complemented (non-normed) topological algebras. The existence of continuous linear maps, in the context of quasi-complemented vector spaces, is a very important issue in their study. Relative to this, we prove that every Hausdorff quasi-complemented locally convex space has continuous linear maps, under which a certain quasi-complemented locally convex space turns to be pre-Hilbert.

Article information

Source
Adv. Oper. Theory, Volume 3, Number 3 (2018), 507-521.

Dates
Received: 5 December 2017
Accepted: 23 January 2018
First available in Project Euclid: 7 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.aot/1518016382

Digital Object Identifier
doi:10.15352/aot.1712-1270

Mathematical Reviews number (MathSciNet)
MR3795097

Zentralblatt MATH identifier
06902449

Subjects
Primary: 46A03: General theory of locally convex spaces
Secondary: 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Keywords
(semi-)quasi-complemented vector space quasi-complementor pseudo-$H$-space automorphically perfect pair

Citation

Haralampidou, Marina; Tzironis, Konstantinos. A Kakutani–Mackey-like theorem. Adv. Oper. Theory 3 (2018), no. 3, 507--521. doi:10.15352/aot.1712-1270. https://projecteuclid.org/euclid.aot/1518016382


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