FINITE REPRESENTABILITY OF HOMOGENEOUS HILBERTIAN OPERATOR SPACES IN SPACES WITH FEW COMPLETELY BOUNDED MAPS

FINITE REPRESENTABILITY OF HOMOGENEOUS HILBERTIAN OPERATOR SPACES IN SPACES WITH FEW COMPLETELY BOUNDED MAPS

For every homogeneous Hilbertian operator space H, we construct a Hilbertian operator space X such that every infinite dimensional subquotient Ƴ of X is completely indecomposable, and fails the Operator Approximation Property, yet H is completely finitely representable in Ƴ. If H satisfies certain c...

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Veröffentlicht in:Journal of operator theory 2009-01, Vol.61 (1), p.3-18
1. Verfasser: OIKHBERG, T.
Format: Artikel
Sprache:eng
Schlagworte:
Abstract spaces
Approximation
Banach space
Hilbert spaces
Integers
Mathematical vectors
Numbers
Scalars
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Zusammenfassung:For every homogeneous Hilbertian operator space H, we construct a Hilbertian operator space X such that every infinite dimensional subquotient Ƴ of X is completely indecomposable, and fails the Operator Approximation Property, yet H is completely finitely representable in Ƴ. If H satisfies certain conditions, we also prove that every completely bounded map on such Ƴ is a compact perturbation of a scalar.
ISSN:0379-4024
1841-7744