(LF)-spaces with more-than-separable quotients

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• 作者：Stephen A. Saxon¹ ; ^{stephen_saxon@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Properly separable quotients ; (LF)-spaces ; Primitive spaces
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：434
• 期：1
• 页码：12-19
• 全文大小：328 K

文摘

The separable quotient problem remains open for Banach spaces. The recent solution for barrelled spaces counters Saxon–Narayanaswami's solution for (LF)-spaces. W.J. Robertson proposed properly separable quotients. We fully answer her quarter-century-old question, proving (LF)-spaces admit properly separable quotients with rare exception. Corollary: Every (LF)-space except φ admits properly separable quotients if and only if Banach's classic separable quotient problem has a positive solution.