Carl's inequality for quasi-Banach spaces

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• 作者：Aicke Hinrichs^a ; ^{aicke.hinrichs@jku.at" class="auth_mail" title="E-mail the corresponding author} ; Anton Kolleck^b ; ¹ ; ^{kolleck@math.tu-berlin.de" class="auth_mail" title="E-mail the corresponding author} ; Jan Vybí ; ral^c ; ² ; ^{vybiral@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Gelfand numbers ; Entropy numbers ; Carl's inequality ; Compressed sensing
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：271
• 期：8
• 页码：2293-2307
• 全文大小：372 K

文摘

We prove that for any two quasi-Banach spaces X and Y   and any α>0$\alpha >0$ there exists a constant 37d49406349fbec548" title="Click to view the MathML source">γ_α>0${\gamma }_{\alpha }>0$ such that holds for all linear and bounded operators d25ba673f0454" title="Click to view the MathML source">T:X→Y$T:X\to Y$. Here e_k(T)$e_k(T)$ is the k-th entropy number of T   and c_k(T)$c_k(T)$ is the k-th Gelfand number of T. For Banach spaces X and Y this inequality is widely used and well-known as Carl's inequality. For general quasi-Banach spaces it is a new result.