4 problems

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The pure-state kernel conjecture for algebraically irreducible representations of quantales
Pure-state kernel conjecture. Every algebraically irreducible representation of $\mathrm{Max\,} A$ has the property that there exists a pure state of $A$ whose kernel is mapped pro…
Conjectureopenoperator-algebras quantales representation-theoryarXiv posted 2 days ago
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Mulvey–Paseka's non-triviality conjecture for algebraically irreducible representations of ${\rm Max}\,A$
Let $A$ be a unital C-algebra. An algebraically irreducible representation of ${\rm Max}\,A$ is a representation that is atomic as a sup-lattice and whose every atom is a generator…
Conjectureopenc-algebras quantales sup-latticesarXiv posted 2 days ago
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Localizability of the nonzero filter in a quantale
Nonzero-filter localizability conjecture. The filter $mid 0$ is localizable over $Q$ .
Conjectureopenlocalization quantalesarXiv posted 2 days ago
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Non-continuity conjecture for the quantale of finitary distance distributions
Let $\Delta^+=\{u\in\Delta\mid u(\infty)=1\}\cup\{0\}$ be the subquantale of finitary distance distributions. Non-continuity conjecture. The suplattice $\Delta^+$ is not continuous…
Conjectureopenfixed-point-theorems probabilistic-metric-spaces quantalesarXiv posted 2 days ago

The pure-state kernel conjecture for algebraically irreducible representations of quantales