Interpolation of Fremlin tensor products and Schur factorization of matrices

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• 作者：Andreas Defant^a ; ^{andreas.defant@uni-oldenburg.de} ; Mieczysł ; aw Mastył ; o^b ; ¹ ; ^{mastylo@amu.edu.pl}
• 关键词：Banach lattice ; Complex interpolation ; Fremlin tensor product ; Regular operator ; Calderó ; n&ndash ; Lozanovskii space
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 出版时间：1 May, 2012
• 年：2012
• 卷：262
• 期：9
• 页码：3981-3999
• 全文大小：183 K

文摘

Within finite dimensional Banach lattices we prove interpolation formulas for the Fremlin tensor product and spaces of regular multilinear forms and operators. We show applications to factorization of matrices with respect to the Schur product. Our results imply various abstract variants of Schur?s classical result, and in particular we extend Pisier?s converse for matrices in finite dimensional -spaces to the setting of complex Calder¨®n interpolation of finite dimensional Banach lattices.