Generalized s-numbers of τ-measurable operators

Pacific Journal of Mathematics

Volumn 123, Issue 2, 1986, Pages 269-300

  Fack, Thierry ^a,b   Kosaki, Hideki ^a,b,c  

^a SORBONNE UNIVERSITÉ   (France)

^b TULANE UNIVERSITY   (United States)

^c KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972546868     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1986.123.269     Document Type: Article

References (34)

1. C. Akemann, J. Anderson, and G. Pedersen, Triangle inequalities in operator algebras, Linear and Multilinear Algebra, 11 (1982), 167-178.
2. L. Brown, Lidskii’s theorem in the type II case, preprint.
3. L. Brown and H. Kosaki, Jensen’s inequality in semi-finite von Neumann algebras, to appear in J. Operator Theory.
4. p-spaces, Colloquim Math., 27 (1973), 83-87.
5. J. Dixmier, Formes linéaires sur un anneau d’opérateurs, Bull. Soc. Math. France, 81 (1953), 9-39.
6. J. Dixmier, Les algébres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann), Gauthier-Villars, Paris, 1968.
7. W. Donoghue, Jr., Monotone Matrix Functions and Analytic Continuation, Springer, Berlin-Heidelberg-New York, 1974.
8. T. Fack, Sur la notion de valeur caractéristique, J. Operator Theory, 7 (1982), 307-333.
9. T. Fack, Proof of the conjecture of A. Grothendieck on the Fuglede-Kadison determinant, J. Funct. Anal., 50 (1983), 215-228.
10. I. C. Gohberg and M. G. Krein, Introduction to linear non-self adjoint operators, Translations of Mathematical Monographs Vol. 18, Amer. Math. Soc., Rhode Island, 1969.
11. A. Grothendieck, Réarrangements de fonctions et inégalités de convexité dans les algèbres de von Neumann munies d’une trace, Séminaire Bourbaki, (1955), 113-01113-13.
12. p-spaces associated with an arbitrary von Neumann algebra, Colloques Internationaux, CNRS, № 274, 175-184.
13. p-spaces), J. Funct. Anal., 56 (1984), 29-78.
14. p-spaces, Trans. Amer. Math. Soc., 283 (1984), 265-282.
15. H. Kosaki, On the continuity of the map φ → |φ| from the predual of a W*-algebra, J. Funct. Anal., 59 (1984), 123-131.
16. p-Fourier transforms in locally compact unimodular groups, Trans. Amer. Math. Soc., 89 (1958), 519-540.
17. p9 Israel J. Math., 5 (1967), 249-271.
18. F. Murray and J. von Neumann, On rings of operators, Ann. of Math., 37 (1936), 116-229.
19. E. Nelson, Notes on non-commutative integration, J. Funct. Anal., 15 (1974), 103-116.
20. A. R. Padmanabhan, Convergence in measure and related results in finite rings of operators, Trans. Amer. Math. Soc., 128 (1967), 359-378.
21. A. R. Padmanabhan, Probabilistic aspects of von Neumann algebras, J. Funct. Anal., 31 (1979), 139-149.
22. W. Rudin, Real and Complex Analysis, McGraw-Hill, 1974.
23. I. Segal, A non-commutative extension of abstract integration, Ann. of Math., 57 (1953), 401-457.
24. B. Simon, Trace Ideals and Their Applications, Cambridge Univ. Press, 1979.
25. M. G. Sonis, On a class of operators with Segal measure on the projectors, Math. USSR Sbomik, 13 (1971), 344-359.
26. E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.
27. F. Stinespring, Integration theorem for gages and duality for unimodular groups, Trans. Amer. Math. Soc., 90 (1959), 15-56.
28. M. Takesaki, Duality for crossed products and structure of von Neumann algebras of type III, Acta Math., 131 (1973), 249-310.
29. M. Takesaki, Theory of Operator Algebras I, Springer, Berlin-Heidelberg-New York, 1979.
30. p-spaces associated with semi-finite von Neumann algebras, Trans. Amer. Math. Soc., 254 (1979), 339-354.
31. p-spaces associated with von Neumann algebras, Copenhagen Univ., 1981.
32. R. C. Thompson, Convex and concave functions of singular values of matrix sums, Pacific J. Math., 66 (1976), 285-290.
33. p-spaces, Proc. Cambridge Philos. Soc., 77 (1975), 91-102.
34. L. Zsido, On the spectral subspaces of locally compact abelian groups of operators, Advances in Math., 36 (1980), 213-276.