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Edit: closed convex hull added. I am trying to understand the state space of $C(K,M_n)=C(K)\otimes M_n$ for $K$ a compact space. My guess would be that these are the closed convex hull of states on $C …

Consider the free product of $\mathbb{Z}/2$ with itself with generators $$ \mathbb{Z}/2*\mathbb{Z}/2=\langle u,v\mid u^2=1=v^2\rangle $$ and regard its group $C^*$-algebra $$ C^*(\mathbb{Z}/2*\mathbb{ …

What are some good sources of examples (and/or the simplest example) for: Pairs of automorphisms $\phi,\psi:A\to A$ over the same base $C^*$-algebra $A$ with non-stably isomorphic crossed products, i. …

From [Donsing-Pitts-2008, theorem 4.8]: For $A\subseteq B$ a regular inclusion, with $A$ abelian, and $E:B\to A$ its unique conditional expectation it holds: The left ideal $$L(E):=\{b\in B:E(b^*b)=0 …

Are there examples of a non-zero C*-algebra which is universally generated by finitely many projections (not all commuting) together with a unit and plus necessarily satisfying some additional relati …

Is the following assertion and the proof below correct, or am I missing something very important? Moreover, would the corollaries be correct then? Besides, I would also appreciate a lot any comment, …

This thread originated from MSE: Approximation Property: Decomposition Given a Banach space $E$. Consider a finite rank operator $F\in\mathcal{F}(X,E)$. Introduce a basis on the finite dimensional …

Problem Given a Banach space $E$. Denote compact sets by $\mathcal{C}$, compact operators by $\mathcal{C}(X,Y)$, and finite rank operators by $\mathcal{F}(X,Y)$. Suppose it has the approximation pro …

This thread originated from MSE: Compact Approximation This is meant as lemma for: Approximation Property Given a Banach space $E$. Denote compact domains by $\mathcal{C}$. Denote compact operator …

Problem Given a C*-algebra $\mathcal{A}$. Consider dynamics $\tau:\mathbb{R}\to\mathrm{Aut}(\mathcal{A})$ and $\tau':\mathbb{R}\to\mathrm{Aut}(\mathcal{A})$. (More precisely, strongly continuous one …

Why do we generalize functions by functionals on Schwartz Spaces, beyond the fact that it simply works? There should be a deeper reason why Schwartz considered functionals. Excited for answers, Alex.