Pointwise tensor products of function spaces

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• 作者：Fé ; lix Cabello S&aacute ; nchez <sup>fcabello@unex.es" class="auth_mailsup>
• 关键词：Function space ; Tensor product ; Nonlinear centralizer ; Exact sequence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：1 October 2014
• 年：2014
• 卷：418
• 期：1
• 页码：317-335
• 全文大小：368 K

文摘

By means of a mixture of linear and nonlinear techniques, the paper treats quasi-Banach function spaces as <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X14001887&_mathId=si1.gif&_user=111111111&_pii=S0022247X14001887&_rdoc=1&_issn=0022247X&md5=332b585da5a356661ae7c0d2b1cd08a0" title="Click to view the MathML source">L<sub>∞sub>span><span class="mathContainer hidden"><span class="mathCode">scroll">sub>L∞sub>span>span>span>-modules and studies the basic algebraical constructions and their interactions, placing the emphasis on tensor products. Sample result: if <span id="mmlsi2" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X14001887&_mathId=si2.gif&_user=111111111&_pii=S0022247X14001887&_rdoc=1&_issn=0022247X&md5=2ef67a4d8d2a8366b141c0010c46f50d" title="Click to view the MathML source">0→Y→X→Z→0span><span class="mathContainer hidden"><span class="mathCode">scroll">0stretchy="false">→Ystretchy="false">→Xstretchy="false">→Zstretchy="false">→0span>span>span> is an exact sequence of <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X14001887&_mathId=si1.gif&_user=111111111&_pii=S0022247X14001887&_rdoc=1&_issn=0022247X&md5=332b585da5a356661ae7c0d2b1cd08a0" title="Click to view the MathML source">L<sub>∞sub>span><span class="mathContainer hidden"><span class="mathCode">scroll">sub>L∞sub>span>span>span>-modules and homomorphisms, where Y   and Z   are function spaces, and V   is another function space, then the tensorized sequence <span id="mmlsi3" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X14001887&_mathId=si3.gif&_user=111111111&_pii=S0022247X14001887&_rdoc=1&_issn=0022247X&md5=eadd9e318dee89bbab98ebb360de4be9" title="Click to view the MathML source">0→Y&otimes;V→X&otimes;V→Z&otimes;V→0span><span class="mathContainer hidden"><span class="mathCode">scroll">0stretchy="false">→Y&otimes;Vstretchy="false">→X&otimes;Vstretchy="false">→Z&otimes;Vstretchy="false">→0span>span>span> is exact too.