1984 | OriginalPaper | Buchkapitel
Grothendieck’s Inequality and the Grothendieck-Lindenstrauss-Pelczynski Cycle of Ideas
verfasst von : Joseph Diestel
Erschienen in: Sequences and Series in Banach Spaces
Verlag: Springer New York
Enthalten in: Professional Book Archive
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In this section we prove a profound inequality due, as the section title indicates, to Grothendieck. This inequality has played a fundamental role in the recent progress in the study of Banach spaces. It was discovered in the 1950s, but its full power was not generally realized until the late 1960s when Lindenstrauss and Pelczynski, in their seminal paper “Absolutely summing operators in ℒp spaces and their applications,” brutally reminded functional analysts of the existence and importance of the powerful ideas and work of Grothendieck. Since the Lindenstrauss-Pelczynski paper, the Grothendieck inequality has seen many proofs; in this, it shares a common feature of most deep and beautiful results in mathematics. The proof we present is an elaboration of one presented by R. Rietz. It is very elementary.