×

Finite dimensional injective operator spaces. (English) Zbl 0962.46042

It is shown that every finite-dimensional injective operator space embeds into a finite-dimensional \(C^\ast\)-algebra \(A\) as a corner, that is, is completely isometrically isomorphic to an operator subspace of the form \(pAp^\perp\) for a projection \(p\in A\). The existence of such an embedding actually happens to be a charaterization of injectivity for finite-dimensional operator spaces. (It is known that in general not every finite-dimensional operator space embeds into a finite-dimensional \(C^\ast\)-algebra.).

MSC:

46L07 Operator spaces and completely bounded maps
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] David P. Blecher, The standard dual of an operator space, Pacific J. Math. 153 (1992), no. 1, 15 – 30. · Zbl 0726.47030
[2] E. G. Effros, Talk at the annual meeting of the A.M.S., San Antonio, January 1999.
[3] E. G. Effros and P. W. Ng, Manuscript in preparation.
[4] Edward G. Effros and Zhong-Jin Ruan, \?\Bbb L_{\?} spaces, Operator algebras and operator theory (Shanghai, 1997) Contemp. Math., vol. 228, Amer. Math. Soc., Providence, RI, 1998, pp. 51 – 77. · Zbl 0929.46048 · doi:10.1090/conm/228/03281
[5] E. G. Effros and Z.-J. Ruan, Dual injective operator spaces, preprint, 1999.
[6] Zhong-Jin Ruan, Injectivity of operator spaces, Trans. Amer. Math. Soc. 315 (1989), no. 1, 89 – 104. · Zbl 0669.46029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.