Uniform factorization for p-compact sets of p-compact linear operators

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• 作者：Erhan Ç ; alışkan^a ; ^{ercalis@yahoo.com.tr" class="auth_mail" title="E-mail the corresponding author} ; Ayşeg&uuml ; l Keten^b ; ¹ ; ² ; ^{aketen@konya.edu.tr" class="auth_mail" title="E-mail the corresponding author} ; ^{aketen@yildiz.edu.tr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Banach spaces ; p-Compact sets ; p-Compact linear operators ; Factorization ; Tensor product ; Homogeneous polynomials
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：437
• 期：2
• 页码：1058-1069
• 全文大小：434 K

文摘

Obtaining a factorization of p-compact linear operators via universal Banach spaces, and using the lifting property of quotient maps for p-compact sets we prove a factorization result for relatively r-compact subsets of p  -compact operators, where thmlsrc">text stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600055X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1600055X&_rdoc=1&_issn=0022247X&md5=c190db0cab9d611f05047c9c5d20e68d" title="Click to view the MathML source">r≥2thContainer hidden">thCode">th altimg="si1.gif" overflow="scroll">r≥2th>, thmlsrc">text stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600055X&_mathId=si2.gif&_user=111111111&_pii=S0022247X1600055X&_rdoc=1&_issn=0022247X&md5=4bf5da707bbb296129b44def67510340" title="Click to view the MathML source">1≤p≤r<∞thContainer hidden">thCode">th altimg="si2.gif" overflow="scroll">1≤p≤r<∞th>. To apply our results to homogeneous polynomials, in particular, we show that relatively p-compact subsets of a Banach space of p-compact operators are collectively p-compact.