On the operator space structure of Hilbert spaces
Bunce, L. J. and Timoney, R. M. (2011) On the operator space structure of Hilbert spaces. Bulletin of the London Mathematical Society, 43 (6). pp. 1205-1218. ISSN 0024-6093
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To link to this article DOI: 10.1112/blms/bdr054
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.