Advances in Operator Theory
- Adv. Oper. Theory
- Volume 3, Number 3 (2018), 507-521.
A Kakutani–Mackey-like theorem
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.
Adv. Oper. Theory, Volume 3, Number 3 (2018), 507-521.
Received: 5 December 2017
Accepted: 23 January 2018
First available in Project Euclid: 7 February 2018
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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