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تسجيل مستخدم جديدSmooth approximation of Lipschitz projections
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Hanfeng Li
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We show that any Lipschitz projection-valued function p on a connected closed Riemannian manifold can be approximated uniformly by smooth projection-valued functions q with Lipschitz constant close to that of p. This answers a question of Rieffel.
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It is shown that for any approximately central (AC) projection $e$ in the Flip orbifold $A_theta^Phi$ (of the irrational rotation C*-algebra $A_theta$), and any modular automorphism $alpha$ (arising from SL$(2,mathbb Z)$), the AC projection $alpha(e)
$ is centrally Murray-von Neumann equivalent to one of the projections $e, sigma(e), kappa(e), kappa^2(e),$ $sigmakappa(e), sigmakappa^2(e)$ in the $S_3$-orbit of $e,$ where $sigma, kappa$ are the Fourier and Cubic transforms of $A_theta$. (The equivalence being implemented by an approximately central partial isometry in $A_theta^Phi$.) For smooth automorphisms $alpha,beta$ of the Flip orbifold $A_theta^Phi$, it is also shown that if $alpha_*=beta_*$ on $K_0(A_theta^Phi),$ then $alpha(e)$ and $beta(e)$ are centrally equivalent for each AC projection $e$.
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Let $X$ be a $d$-dimensional random vector and $X_theta$ its projection onto the span of a set of orthonormal vectors ${theta_1,...,theta_k}$. Conditions on the distribution of $X$ are given such that if $theta$ is chosen according to Haar measure on
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In this short note, we prove that for a $C^*$-algebra $aa$ generated by $n$ elements, $M_{k}(tilde{aa})$ is generated by $k$ mutually unitarily equivalent and almost mutually orthogonal projections for any $kge de(n)=minbig{kinmathbb N,|,(k-1)(k-2)ge
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