Contractively complemented subspaces of pre-symmetric spaces
Matthew Neal, Bernard Russo

TL;DR
This paper extends classical results on contractive projections in $L^1$-spaces and preduals of von Neumann algebras to the broader setting of preduals of $JBW^*$-triples, identifying conditions under which such projections exist.
Contribution
It significantly broadens the scope of previous results by establishing the existence of contractive projections for subspaces of preduals of $JBW^*$-triples, with specific restrictions.
Findings
Existence of contractive projections for subspaces of preduals of $JBW^*$-triples.
The result holds under the condition that the target $JBW^*$-triple does not contain a certain type of summand.
The theorem generalizes earlier results from $L^1$-spaces and von Neumann algebra preduals.
Abstract
In 1965, Ron Douglas proved that if is a closed subspace of an -space and is isometric to another -space, then is the range of a contractive projection on the containing -space. In 1977 Arazy-Friedman showed that if a subspace of is isometric to another -space (possibly finite dimensional), then there is a contractive projection of onto . In 1993 Kirchberg proved that if a subspace of the predual of a von Neumann algebra is isometric to the predual of another von Neumann algebra, then there is a contractive projection of the predual of onto . We widen significantly the scope of these results by showing that if a subspace of the predual of a -triple is isometric to the predual of another -triple , then there is a contractive projection on the predual of with range , as long as does not…
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory
