Non-isomorphism of $L_p$-spaces associated with finite and infinite von Neumann algebras
HTML articles powered by AMS MathViewer
- by F. A. Sukochev PDF
- Proc. Amer. Math. Soc. 124 (1996), 1517-1527 Request permission
Abstract:
If $(M_{1},\tau _{1})$ is a finite von Neumann algebra and if $(M_{2},\tau _{2})$ is an infinite (semifinite) von Neumann algebra, then $L_{p}(M_{1},\tau _{1})$ and $L_{p}(M_{2},\tau _{2})$ are non-isomorphic for all $p\in (1,\infty ), p\neq 2$ .References
- J. Arazy and J. Lindenstrauss, Some linear topological properties of the spaces $C_{p}$ of operators on Hilbert space, Compositio Math. 30 (1975), 81–111. MR 372669
- S. Banach, Théorie des opérations linéaires, Warszawa, 1932.
- Vladimir I. Chilin, Arthur M. Medzhitov, and Pheodor A. Sukochev, Isometries of noncommutative Lorentz spaces, Math. Z. 200 (1989), no. 4, 527–545. MR 987585, DOI 10.1007/BF01160954
- Vladimir I. Chilin, Andrei V. Krygin, and Pheodor A. Sukochev, Local uniform and uniform convexity of noncommutative symmetric spaces of measurable operators, Math. Proc. Cambridge Philos. Soc. 111 (1992), no. 2, 355–368. MR 1142755, DOI 10.1017/S0305004100075459
- Peter G. Dodds, Theresa K.-Y. Dodds, and Ben de Pagter, Noncommutative Banach function spaces, Math. Z. 201 (1989), no. 4, 583–597. MR 1004176, DOI 10.1007/BF01215160
- Peter G. Dodds, Theresa K.-Y. Dodds, and Ben de Pagter, Noncommutative Köthe duality, Trans. Amer. Math. Soc. 339 (1993), no. 2, 717–750. MR 1113694, DOI 10.1090/S0002-9947-1993-1113694-3
- Thierry Fack, Type and cotype inequalities for noncommutative $L^p$-spaces, J. Operator Theory 17 (1987), no. 2, 255–279. MR 887222
- Thierry Fack and Hideki Kosaki, Generalized $s$-numbers of $\tau$-measurable operators, Pacific J. Math. 123 (1986), no. 2, 269–300. MR 840845, DOI 10.2140/pjm.1986.123.269
- M. I. Kadec and A. Pełczyński, Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$, Studia Math. 21 (1961/62), 161–176. MR 152879, DOI 10.4064/sm-21-2-161-176
- S. G. Kreĭn, Yu. Ī. Petunīn, and E. M. Semënov, Interpolation of linear operators, Translations of Mathematical Monographs, vol. 54, American Mathematical Society, Providence, R.I., 1982. Translated from the Russian by J. Szűcs. MR 649411
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8
- —, Classical Banach spaces II. Function spaces, Springer-Verlag, New-York, 1979.
- Charles A. McCarthy, $c_{p}$, Israel J. Math. 5 (1967), 249–271. MR 225140, DOI 10.1007/BF02771613
- F. A. Sukochev and V. I. Chilin, Symmetric spaces on semifinite von Neumann algebras, Soviet Math. Dokl. 42 (1992), 97–101.
- —, Weak convergence in non-commutative symmetric spaces, J. Operator Theory 31 (1994), 35–65.
- Şerban Strătilă and László Zsidó, Lectures on von Neumann algebras, Editura Academiei, Bucharest; Abacus Press, Tunbridge Wells, 1979. Revision of the 1975 original; Translated from the Romanian by Silviu Teleman. MR 526399
- Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728, DOI 10.1007/978-1-4612-6188-9
- Keiichi Watanabe, On isometries between noncommutative $L^p$-spaces associated with arbitrary von Neumann algebras, J. Operator Theory 28 (1992), no. 2, 267–279. MR 1273046
- Xu, Convexité uniforme des espaces symmétriques d’opérateurs mesurables, C. R. Acad. Sci. Paris. Serie $I$ 309 (1989), 251–254.
- F. J. Yeadon, Isometries of noncommutative $L^{p}$-spaces, Math. Proc. Cambridge Philos. Soc. 90 (1981), no. 1, 41–50. MR 611284, DOI 10.1017/S0305004100058515
Additional Information
- F. A. Sukochev
- Affiliation: Department of Mathematics and Statistics, School of Information Science and Technology, The Flinders University of South Australia, GPO Box 2100, Adelaide, SA 5001, Australia
- MR Author ID: 229620
- Email: sukochev@ist.flinders.edu.au
- Received by editor(s): October 31, 1994
- Additional Notes: Research supported by the Australian Research Council.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1517-1527
- MSC (1991): Primary 46L50; Secondary 47D15, 46E30
- DOI: https://doi.org/10.1090/S0002-9939-96-03279-0
- MathSciNet review: 1317053