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Creators/Authors contains: "Blecher, David P"

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  1. ; ; ; (, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas)
    We prove that a subspace of a real JBW∗-triple is an M-summand if and only if it is a weak∗-closed triple ideal. As a consequence, M-ideals of real JB∗-triples correspond to norm-closed triple ideals. As in the setting of complex JB∗-triples, a geometric property is characterized in purely algebraic terms. This is a newfangled treatment of the classical notion of M-ideal in the real setting, by a completely new approach necessitated by the unfeasibility of the known arguments from the setting of complex C∗-algebras and JB∗-triples. The results in this note also provide a full characterization of all M-ideals in real C∗-algebras, real JB∗-algebras and real TROs. 
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    Free, publicly-accessible full text available January 1, 2026
  2. (, Studia Mathematica)
    We verify that a large portion of the theory of complex operator spaces and operator algebras (as represented by the 2004 book by the author and Le Merdy for specificity) transfers to the real case. We point out some of the results that do not work in the real case. We also discuss how the theory and standard constructions interact with the complexification, which is often as important, but sometimes much less obvious. For example, we develop the real case of the theory of operator space multipliers and the operator space centralizer algebra, and discuss how these topics connect with complexifi- cation. This turns out to differ in some important details from the complex case. We also characterize real structure in complex operator spaces and give ‘real’ characterizations of some of the most important objects in the subject. 
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