Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the split property for inclusions of $W^{*}$-algebras

Author: Francesco Fidaleo
Journal: Proc. Amer. Math. Soc. 130 (2002), 121-127
MSC (2000): Primary 46L37; Secondary 46L07, 46L10
Published electronically: June 8, 2001
MathSciNet review: 1855628
Full-text PDF

Abstract | References | Similar Articles | Additional Information


A characterization of the quasi-split property for an inclusion of $W^*$-algebras in terms of the metrically nuclear maps is established. This result extends the known characterization relative to inclusions of $W^*$-factors. An application to type $I$ von Neumann algebras is also presented.

References [Enhancements On Off] (What's this?)

  • 1. Buchholz D., D'Antoni C., Fredenhagen K. The universal structures of local algebras, Commun. Math. Phys. 111 (1987), 123-135. MR 88j:46055
  • 2. Buchholz D., D'Antoni C., Longo, R. Nuclear maps and modular structures I, J. Funct. Anal. 88 (1990), 233-250. MR 91f:46080
  • 3. Buchholz D., D'Antoni C., Longo R. Nuclear maps and modular structures II, Commun. Math. Phys. 129 (1990), 115-138. MR 91k:81081
  • 4. Connes A., Jones V. F. R. Property $T$ for von Neumann algebras, Bull. London Math. Soc. 17 (1985), 57-62. MR 86a:46083
  • 5. D'Antoni C., Longo R. Interpolation by type I factors and the flip automorphism, J. Funct. Anal. 51 (1983), 361-371. MR 84k:46047
  • 6. Effros E., Ruan Z.-J. On approximation properties for operator spaces, International J. Math. 1 (1990), 163-187. MR 92g:46089
  • 7. Effros E., Ruan Z.-J. Mapping spaces and liftings of operator spaces, Proc. London Math. Soc. 69 (1994), 171-197. MR 96c:46074a
  • 8. Fidaleo F. Operator space structures and the split property, J. Operator Theory 31 (1994), 207-218. MR 97a:46069
  • 9. Fidaleo F. Some operator ideals in non-commutative functional analysis, Z. Anal. Anwendungen 17 (1998), 759-776. MR 99i:46041
  • 10. Haagerup U. $L^p$-spaces associated with an arbitrary von Neumann algebra, Colloques internationaux CNRS 274 (1979) 175-184. MR 81e:46050
  • 11. Paulsen V. I. Completely bounded maps and dilations, Longman Scientific & Technical (1986). MR 88h:46111
  • 12. Ruan Z.-J., Subspaces of $C^*$-algebras, J. Funct. Anal. 76 (1988), 217-230. MR 89h:46082
  • 13. Stratila S., Zsido L. Lectures on von Neumann algebras, Abacus Press (1979). MR 81j:46089
  • 14. Summers S. J. On the independence of local algebras in Quantum Field Theory, Rev. Math. Phys. 2 (1990), 201-247. MR 92c:81086
  • 15. Takesaki M. Theory of operator algebras I, Springer (1979). MR 81e:46038

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L37, 46L07, 46L10

Retrieve articles in all journals with MSC (2000): 46L37, 46L07, 46L10

Additional Information

Francesco Fidaleo
Affiliation: Dipartimento di Matematica and Centro Interdisciplinare Vito Volterra, II Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy

Keywords: Classifications, factors, linear spaces of operators
Received by editor(s): June 8, 2000
Published electronically: June 8, 2001
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society