Projection operators nearly orthogonal to their symmetries

详细信息    查看全文

• 作者：Sam Walters ^{walters@unbc.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hilbert space ; Norm approximation ; C*-algebras ; Automorphisms ; Projections ; Orthogonality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1356-1361
• 全文大小：238 K

文摘

For any order 2 automorphism α of a C*-algebra A (a symmetry of A), we prove that for each projection e   such that $\Vert e\alpha (e)\Vert \le \frac{9}{20}$, there exists a projection q   with qα(q)=0$q\alpha (q)=0$ satisfying the norm estimate In other words, if e   is a projection that is “nearly orthogonal” to its symmetry α(e)$\alpha (e)$ in the sense that the norm ‖eα(e)‖$\Vert e\alpha (e)\Vert$ is no more than dd304">$\frac{9}{20}$, then e can be approximated by a projection q   that is exactly orthogonal to its symmetry in a fairly optimal fashion. (Optimal in the sense that the first term in the estimate satisfies $\frac{1}{2}\Vert e\alpha (e)\Vert \le \Vert e-q\Vert$ for any such q.)