Range tripotents and order in JBW*-triples

• Autorzy: Lina Oliveira
• Języki publikacji: EN

Abstrakty

EN

In a JBW*-triple, i.e., a symmetric complex Banach space possessing a predual, the set of tripotents is naturally endowed with a partial order relation. This work is mainly concerned with this partial order relation when restricted to the subset 𝓡(A) of tripotents in a JBW*-triple B formed by the range tripotents of the elements of a JB*-subtriple A of B. The aim is to present recent developments obtained for the poset 𝓡(A) of the range tripotents relative to A, whilst also providing the necessary account of the general theory of the lattice of tripotents. Although the leitmotiv might be described as seeking to find conditions under which the supremum of a subset of range tripotents relative to A is itself a range tripotent relative to A, other properties are also investigated. Amongst these is the relation between range tripotents and partial isometries and support projections in W*-algebras.

Kategorie tematyczne

• 46L70: Nonassociative selfadjoint operator algebras
• 17C65: Jordan structures on Banach spaces and algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 233-246

Daty

wydano

2010

Twórcy

autor

Lina Oliveira

• Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

Identyfikatory

DOI

10.4064/bc91-0-14