The operator Hilbert space OH, complex interpolation, and tensor norms
In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual…
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- Full title :The operator Hilbert space OH, complex interpolation, and tensor norms / Gilles Pisier.
Summary
In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]OH) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.
Read More ↓Edition Statements
- Publication Date:©1996.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©1996.
Notes
"July 1996, volume 122, number 585 (end of volume)."
The Physical Object
- Description:viii, 103 pages ; : 26 cm.
Edition Identifiers
- ISBN:082180474X, 9780821804742
- oclc:ocm34472711
- LC Classification:QA3
- Dewey Decimal:510 s
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