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Let $G$ be a finite group, and let $T_1,T_2 \le G$ be conjugate subgroups. Set $$ A := T_1T_2 \cap T_2T_1. $$ For a subset $S \subseteq G$, let $M_S$ denote...
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Let $\gamma$ be the standard Gaussian measure on $\mathbb{R}^\infty$, i.e. the product of the standard Gaussian measures on $\mathbb{R}$. It is known that $$...
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I want to find an example of a bijective operator on a Hilbert space $T : \mathfrak{H} \rightarrow \mathfrak{H} $ such that its inverse $T^{-1}$ is not...
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Let $p\in [1,\infty]$, and $\Omega\subset\mathbb{R}^N$ a bounded, open and connected set. If $u\in W^{1,p}((0,T);L^{p}(\Omega))$ and...
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I am interested in the following Boolean-ring question, motivated by a renorming problem for Banach spaces of density $\omega_1$. Let $\mathfrak A$ be a...
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For example in $C^\ast$-algebras by J. Dixmier and A user's guide to operator algebras by P. Fillmore there exist the following nomenclature: A continuous...
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Let $\gamma:[0,1]\to\mathbb{R}^N$ be a continuous rectifiable curve and $\ell(\gamma)$ be its length. Also denote $\Gamma=\{\gamma(t)|\ t\in [0,1]\}$ the image...
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It is well known that finite-dimensional matrix algebras $M_n(\mathbb{C})$ are classified (up to isomorphism) by the prime factorization of $n$, and that UHF...
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Given a $C^*$ algebra $A$ with a fixed (left) representation on a given Hilbert space $H$, is there any way to see if a state $\phi:A\to\mathbb{C}$ is a vector...
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Let $G$ be a $p$-adic group. $(\pi, V)$ is a smooth admissible representation of $G$, with its contragredient $(\pi^\vee,V^\vee)$. For $v\in V, \tilde{v}\in...
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Assume that the axiom of choice and continuum hypothesis hold. I will call a discrete probability space $(X,2^X,\mu)$ diffused if $\mu(\{x\})=0$ for each $x\in...
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Let $G$ be a reductive group over real numbers or p-adic field. We use $\mathcal{A}$ to denote the reduced group C* algebra of $G$. Let $\mathcal{B}$ be the...
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I am reformulating a question from MSE that did not receive any answers so far, hoping that it will get an answer here. Let $X$, $Y$ and $Z$ be Banach spaces....
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I have a question about the consistency strength of a renorming problem that, as far as I understand, goes back to Avilés. Avilés asked whether there exists,...
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