Positivity and the Michael's Problem
Cone, Féchet space, order continuity, Riesz space, seminorm, Banach lattice, Fréchet lattice, Michael's problem, Complex cone, Gelfand transform, Automatic continuity.
Abstract
We define an order on \(\mathbb { C }\) that makes it a Banach lattice.
Having established properties of this order, we shall use them to
provide a brief proof of the solution to the problem posed by E. Michael
in 1952 [8], which was resolved in [6] in 2024 using theorems of
functional analysis.
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References
C. D. Aliprantis, K. C. Border (2006) Infinite Dimensional Analysis. Third Edition.
C. D. Aliprantis, R. Tourky (2007) Cones and Duality. Graduate Studies in Mathematics, Volume 84. 84.
H. Goldmann (1990) Uniform Fréchet Algebras. 162.
J. L. Kelley (1955) General topology. 27.
J. L. Kelley, R. L. Vaught (1953) The positive cone in Banach algebras. 74, 44-55.
M. Laayouni (2024) On the automatic continuity on Fréchet algebras. 16(2), 41-47.
E. Langford, C. D. Aliprantis (1974) Regularity Propreties of Quotient Riesz Seminorms. 199-212.
E. A. Michael (1952) Locally Multiplicatively-Convex Topological Algebras. 11.
S. Sherman (1951) Non-negativeobservables aresquares. 2, 31-33.
Published
2026-07-16
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