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A characterization of maximal regular ideals in lmc algebras

100%
Fragoulopoulou M.
Studia Mathematica
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1992
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tom 103
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nr 1
41-49
EN
A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.
2
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The Shirali-Ford theorem as a consequence of Ptak theory for hermitian Banach algebras

100%
Fragoulopoulou M.
Studia Mathematica
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2002
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tom 150
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nr 2
121-132
EN
A simple application of Pták theory for hermitian Banach algebras, combined with a result on normed Q-algebras, gives a non-technical new proof of the Shirali-Ford theorem. A version of this theorem in the setting of non-normed topological algebras is also provided.
3
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Old and new results on Allan's GB*-algebras

51%
Fragoulopoulou M., Inoue A., Kürsten K.-D.
Banach Center Publications
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2010
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tom 91
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nr 1
169-178
EN
This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication of 𝓐₀ jointly continuous. We conclude that such a completion is a GB*-algebra over the τ-closure of the unit ball of 𝓐₀[||·||₀]. Further, we discuss some consequences of this result; we briefly comment the case when τ makes the multiplication of 𝓐₀ separately continuous and illustrate the results by examples.
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