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On the operator space structure of Hilbert spaces
Author(s) -
Bunce Leslie J.,
Timoney Richard M.
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdr054
Subject(s) - mathematics , linear subspace , operator (biology) , hilbert space , pure mathematics , operator space , isometry (riemannian geometry) , isomorphism (crystallography) , quasinormal operator , compact operator on hilbert space , shift operator , finite rank operator , nuclear operator , injective function , compact operator , space (punctuation) , operator theory , strictly singular operator , banach space , computer science , biochemistry , chemistry , crystal structure , programming language , repressor , transcription factor , extension (predicate logic) , gene , crystallography , operating system
Operator spaces of Hilbertian JC *‐triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite‐dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite‐dimensional subspaces. Injective envelopes are explicitly computed.