journal article
Mar 01, 1995
Bilinear forms on exact operator spaces andB(H)⊗B(H)
Geometric and Functional Analysis
Vol. 5
No. 2
pp. 329-363
·
Springer Science and Business Media LLC
Topics
No keywords indexed for this article. Browse by subject →
References
41
[1]
[AO]C. Akemann, P. Ostrand, Computing norms in group,C *-algebras, Amer. J. Math. 98 (1976), 1015–1047.
10.2307/2374039
[2]
[B]R. Baire, Sur les fonctions des variables réelles, Ann. di Mat. 3∶3 (1899), 1–123.
10.1007/bf02419243
[3]
[Bl1]D. Blecher, Tensor products of operator spaces II, Canadian J. Math. 44 (1992), 75–90.
10.4153/cjm-1992-004-5
[4]
[Bl2]D. Blecher, The standard dual of an operator space, Pacific J. Math. 153 (1992), 15–30.
10.2140/pjm.1992.153.15
[5]
[Bl3]D. Blecher, Tracially completely bounded multilinear maps onC *-algebras, Journal of the London Mathematical Society 39 (1989), 514–524.
10.1112/jlms/s2-39.3.514
[6]
[BlP]D. Blecher, V. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991) 262–292.
10.1016/0022-1236(91)90042-4
[7]
[dCH]J. de Cannière, U. Haagerup, Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups, Amer. J. Math. 107 (1985), 455–500.
10.2307/2374423
[8]
[dHaV]P. de la Harpe, A. Valette, La Propriété T de Kazhdan pour les Groupes Localement Compacts, Astérisque, Soc. Math. France 175 (1989).
[9]
[EH]E. Effros, U. Haagerup, Lifting problems and local reflexivity forC *-algebras, Duke Math. J. 52 (1985), 103–128.
10.1215/s0012-7094-85-05207-x
[10]
[ER1]E. Effros, Z. J. Ruan, A new approach to operator spaces, Canadian Math. Bull. 34 (1991), 329–337.
10.4153/cmb-1991-053-x
[11]
[ER2]E. Effros, Z.J. Ruan, On the abstract characterization of operator spaces, Proc. Amer. Math. Soc. 119 (1993), 579–584.
10.1090/s0002-9939-1993-1163332-4
[12]
[H1]U. Haagerup, The Grothendieck inequality for bilinear forms onC *-algebras, Advances in Math. 56 (1985), 93–116.
10.1016/0001-8708(85)90026-x
[13]
[H2]U. Haagerup, An example of a non-nuclearC *-algebra which has the metric approximation property, Invent. Math. 50 (1979), 279–293.
10.1007/bf01410082
[14]
[H3]U. Haagerup, Injectivity and decomposition of completely bounded maps, in “Operator algebras and their connection with Topology and Ergodic Theory”, Springer Lecture Notes in Math. 1132 (1985), 170–222.
10.1007/bfb0074885
[15]
[HPi]U. Haagerup, G. Pisier, Bounded linear operators betweenC *-algebras, Duke Math. J. 71 (1993), 889–925.
10.1215/s0012-7094-93-07134-7
[16]
[I]T. Itoh, On the completely bounded maps of aC *-algebra to its dual space, Bull. London Math. Soc. 19 (1987), 546–550.
10.1112/blms/19.6.546
[17]
[K1]E. Kirchberg, On subalgebras of the CAR-algebra, to appear in J. Funct. Anal.
[18]
[K2]E. Kirchberg, On non-semisplit extensions, tensor products and exactness of groupC *-algebras, Invent. Math. 112 (1993), 449–489.
10.1007/bf01232444
[19]
[K3]E. Kirchberg, Commutants of unitaries in UHF algebras and functorial properties of exactness, to appear in J. reine angew. Math.
[20]
[Kr]J. Kraus, The slice map problem and approximation properties, J. Funct. Anal. 102 (1991), 116–155.
10.1016/0022-1236(91)90138-u
[21]
[Ku]W. Kuratowski, Topology, Vol. 1. (New edition translated from the French), Academic Press, New-York 1966.
[22]
[Kw]S. Kwapień, On operators factorizable throughL p-spaces, Bull. Soc. Math. France, Mémoire 31–32 (1972), 215–225.
10.24033/msmf.86
[23]
[L]C. Lance, On nuclearC *-algebras, J. Funct. Anal. 12 (1973), 157–176.
10.1016/0022-1236(73)90021-9
[24]
[P1]V. Paulsen, Completely bounded maps and dilations, Pitman Research Notes 146. Pitman Longman (Wiley) 1986.
[25]
[P2]V. Paulsen, Representation of function algebras, Abstract operator spaces and Banach space geometry, J. Funct. Anal. 109 (1992), 113–129.
10.1016/0022-1236(92)90014-a
[26]
[P3]V. Paulsen, The maximal operator space of a normed space, to appear.
[27]
[Pi1]G. Pisier, Exact operator spaces, Colloque sur les algèbres d'opérateurs, Astérisque, Soc. Math. France, to appear.
[28]
[Pi2]G. Pisier, Factorization of Linear Operators and the Geometry of Banach Spaces, CBMS (Regional conferences of the A.M.S.) 60, (1986);
10.1090/cbms/060
[29]
Reprinted with corrections 1987.
10.1215/01636545-1987-39-10
[30]
[Pi3]G. Pisier, The operator Hilbert spaceOH, complex interpolation and tensor norms, submitted to Memoirs Amer. Math. Soc.
[31]
[Pi4]G. Pisier, Factorization of operator valued analytic functions, Advances in Math. 93 (1992), 61–125.
10.1016/0001-8708(92)90025-g
[32]
[Pi5]G. Pisier, Projections from a von Neumann algebra onto a subalgebra, Bull. Soc. Math. France, to appear.
10.24033/bsmf.2254
[33]
[R]Z. J. Ruan, Subspaces ofC *-algebras, J. Funct. Anal. 76 (1988), 217–230.
10.1016/0022-1236(88)90057-2
[34]
[S]S. Sakai,C *-algebras andW *-algebras, Springer Verlag New-York, 1971.
10.1007/978-3-642-61993-9
[35]
[Sm]R.R. Smith, Completely bounded maps betweenC *-algebras, J. London Math. Soc. 27 (1983), 157–166.
10.1112/jlms/s2-27.1.157
[36]
[T]M. Takesaki, Theory of Operator Algebras I, Springer-Verlag New-York 1979.
10.1007/978-1-4612-6188-9
[37]
[Tr]S. Trott, A pair of generators for the unimodular group, Canad. Math. Bull. 3 (1962), 245–252.
10.4153/cmb-1962-024-x
[38]
[Vo]D. Voiculescu, Property T and approximation of operators, Bull. London Math. Soc. 22 (1990), 25–30.
10.1112/blms/22.1.25
[39]
[VoDN]D. Voiculescu, K. Dykema, A. Nica, Free random variables, CRM Monograph Series, 1, Amer. Math. Soc., Providence RI.
[40]
[W1]S. Wassermann, On tensor products of certain groupC *-algebras, J. Funct. Anal. 23 (1976), 239–254.
10.1016/0022-1236(76)90050-1
[41]
[W2]S. Wassermann, ExactC *-algebras and related topics, Lecture Notes Series 19, Seoul National University, 1994.
Metrics
44
Citations
41
References
Details
- Published
- Mar 01, 1995
- Vol/Issue
- 5(2)
- Pages
- 329-363
- License
- View
Authors
Cite This Article
M. Junge, G. Pisier (1995). Bilinear forms on exact operator spaces andB(H)⊗B(H). Geometric and Functional Analysis, 5(2), 329-363. https://doi.org/10.1007/bf01895670
Related
You May Also Like
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
J. Bourgain · 1993
786 citations
Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
J. Bourgain · 1993
566 citations