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Non-commutative generalisations of Urysohn's lemma and hereditary inner ideals by Francisco J. Fernández-Polo; Antonio M. Peralta is a Mathematics article available to read on EtoBox.

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We establish several generalisations of Urysohn's lemma in the setting of JB \* -triples which provide full answers to Problems 1.12 and 1.13 in Fernández-Polo and Peralta (2007) [22]. These results extend the previous generalisations obtained by C.A. Akemann, G.K. Pedersen and L.G. Brown in the setting of C \* -algebras. A generalised Kadison's transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in JBW \* -triples. We introduce the notion of positively open tripotent in the bidual of a JB \* -triple as an extension of a concept which was already considered in the setting of ternary rings of operators. We investigate the connections appearing between positively open tripotents and hereditary inner ideals.

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Author

Francisco J. Fernández-Polo; Antonio M. Peralta

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)