Completely positive compact operators on non-commutative symmetric spaces

Completely positive compact operators on non-commutative symmetric spaces

Under natural conditions, it is shown that a completely positive operator between two non-commutative symmetric spaces of τ-measurable operators which is dominated in the sense of complete positivity by a completely positive compact operator is itself compact.

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2010-12, Vol.14 (4), p.665-679
Hauptverfasser: Dodds, P. G., de Pagter, B.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Banach spaces
Calculus of Variations and Optimal Control
Optimization
Econometrics
Exact sciences and technology
Fourier Analysis
Hilbert space
Integrals
Lattice theory
Mathematical analysis
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Sciences and techniques of general use
Studies
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Beschreibung
Zusammenfassung:Under natural conditions, it is shown that a completely positive operator between two non-commutative symmetric spaces of τ-measurable operators which is dominated in the sense of complete positivity by a completely positive compact operator is itself compact.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-010-0073-9