Non-axiomatizability of real spectra in $\mathcal{L}_\infty \lambda $

Timothy Mellor; Marcus Tressl

Displaying similar documents to “Non-axiomatizability of real spectra in $ℒ_{\infty} λ$ ”

Two classes of locally compact sober spaces.

Belaid, Karim, Echi, Othman, Gargouri, Riyadh (2005)

International Journal of Mathematics and Mathematical Sciences

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An up-spectral space need not be $A$ -spectral.

Echi, Othman, Gargouri, Riyadh (2004)

The New York Journal of Mathematics [electronic only]

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Spectral Real Semigroups

M. Dickmann, A. Petrovich (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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The notion of a was introduced in [8] to provide a framework for the investigation of the theory of (diagonal) quadratic forms over commutative, unitary, semi-real rings. In this paper we introduce and study an outstanding class of such structures, that we call (SRS). Our main results are: (i) The existence of a natural functorial duality between the category of SRSs and that of hereditarily normal spectral spaces; (ii) Characterization of the SRSs as the real semigroups whose representation...

Eventually positive elements in ordered Banach algebras

Gerd Herzog, Peer C. Kunstmann (2023)

Commentationes Mathematicae Universitatis Carolinae

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In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since...