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Reduced Products of Collapsing Algebras
Milo\v{s} S. Kurili\'c
https://arxiv.org/abs/2403.17930 https://arxiv.org/pdf/2403.17930<…

Reduced Products of Collapsing Algebras
$\mathop{\rm rp}\nolimits ({\mathbb B})$ denotes the reduced power ${\mathbb B}^ω/Φ$ of a Boolean algebra ${\mathbb B}$, where $Φ$ is the Fréchet filter $Φ$ on $ω$. We investigate iterated reduced powers ($\mathop{\rm rp}\nolimits ^0 ({\mathbb B})={\mathbb B}$ and $\mathop{\rm rp}\nolimits ^{n+1} ({\mathbb B} )=\mathop{\rm rp}\nolimits (\mathop{\rm rp}\nolimits ^n ({\mathbb B}))$) of collapsing algebras and our main intention is to classify the algebras $\mathop{\rm rp}\nolimits ^n (\math…

Der 29-jährige Noland Arbaugh, der seit einem Tauchunfall von der Schulter abwärts gelähmt ist, konnte dank des Chips die Züge beim Schachspiel mit seinen Gedanken steuern. ♟️🧠
Zum Artikel: https://heise.de/-9661223?wt_mc=sm.red.ho.mastodon.ma…

Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
Eva-Maria Hekkelman, Edward McDonald, Teun D. H. van Nuland
https://arxiv.org/abs/2404.16338

Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
We push the definition of multiple operator integrals (MOIs) into the realm of unbounded operators, using the pseudodifferential calculus from the works of Connes and Moscovici, Higson, and Guillemin. This in particular provides a natural language for operator integrals in noncommutative geometry. For this purpose, we develop a functional calculus for these pseudodifferential operators. To illustrate the power of this framework, we provide a pertubative expansion of the spectral action for regu…

Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
Eva-Maria Hekkelman, Edward McDonald, Teun D. H. van Nuland
https://arxiv.org/abs/2404.16338

Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
We push the definition of multiple operator integrals (MOIs) into the realm of unbounded operators, using the pseudodifferential calculus from the works of Connes and Moscovici, Higson, and Guillemin. This in particular provides a natural language for operator integrals in noncommutative geometry. For this purpose, we develop a functional calculus for these pseudodifferential operators. To illustrate the power of this framework, we provide a pertubative expansion of the spectral action for regu…