اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSmooth approximation of Lipschitz projections
117
0
0.0
(
0
)
تأليف
Hanfeng Li
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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 $e$.
We develop a general framework for reflexivity in dual Banach spaces, motivated by the question of when the weak* closed linear span of two reflexive masa-bimodules is automatically reflexive. We establish an affirmative answer to this question in a
number of cases by examining two new classes of masa-bimodules, defined in terms of ranges of masa-bimodule projections. We give a number of corollaries of our results concerning operator and spectral synthesis, and show that the classes of masa-bimodules we study are operator synthetic if and only if they are strong operator Ditkin.
We develop a symbol calculus for normal bimodule maps over a masa that is the natural analogue of the Schur product theory. Using this calculus we are able to easily give a complete description of the ranges of contractive normal bimodule idempotents
that avoids the theory of J*-algebras. We prove that if $P$ is a normal bimodule idempotent and $|P| < 2/sqrt{3}$ then $P$ is a contraction. We finish with some attempts at extending the symbol calculus to non-normal maps.
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
the Stiefel manifold, the bounded-Lipschitz distance from $X_theta$ to a Gaussian distribution is concentrated at its expectation; furthermore, an explicit bound is given for the expected distance, in terms of $d$, $k$, and the distribution of $X$, allowing consideration not just of fixed $k$ but of $k$ growing with $d$. The results are applied in the setting of projection pursuit, showing that most $k$-dimensional projections of $n$ data points in $R^d$ are close to Gaussian, when $n$ and $d$ are large and $k=csqrt{log(d)}$ for a small constant $c$.
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 $kge de(n)=minbig{kinmathbb N,|,(k-1)(k-2)ge
2nbig}$. Then combining this result with recent works of Nagisa, Thiel and Winter on the generators of $C^*$--algebras, we show that for a $C^*$-algebra $aa$ generated by finite number of elements, there is $dge 3$ such that $M_d(tilde A)$ is generated by three mutually unitarily equivalent and almost mutually orthogonal projections. Furthermore, for certain separable purely infinite simple unital $C^*$--algebras and $AF$--algebras, we give some conditions that make them be generated by three mutually unitarily equivalent and almost mutually orthogonal projections.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
