Symmetric functionals and singular traces

Positivity

Volumn 2, Issue 1, 1998, Pages 47-75

  Dodds, P G ^a   De Pagter, B ^b   Semenov, E M ^c   Sukochev, F A ^a  

^a FLINDERS UNIVERSITY   (Australia)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c VORONEZH STATE UNIVERSITY   (Russian Federation)

Author keywords

Marcinkiewicz space; Singular trace; Symmetric functional; Symmetric operator space

Indexed keywords

EID: 22044443418     PISSN: 13851292     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009720826217     Document Type: Article

References (25)

1. S. Albeverio, D. Guido, A. Ponosov and S. Scarlatti, Singular traces and compact operators, J. Funct. Anal. 137 (1996), 281-302.
2. M. Braverman and A. Mekler, The Hardy-Littlewood property for symmetric spaces, Sib. Mat. Zhur. 18 (1977) 522-540 (Russian).
3. C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988.
4. A. Connes, Noncommutative Geometry, Academic Press, 1994.
5. V.I. Chilin and F.A. Sukochev, Symmetric spaces over semifinite von Neumann algebras, Soviet Math. Dokl. 42 (1991), 97-101.
6. V.I. Chilin and F.A. Sukochev, Weak convergence in non-commutative symmetric spaces, J. Operator Theory 31 (1994), 35-65.
7. J. Dixmier, Existence de traces non normales, C.R. Acad. Sci. Paris 262 (1966) A1107-A1108.
8. P.G. Dodds, T.K. Dodds and B. de Pagter, Non-commutative Banach function spaces, Math. Z. 201 (1989), 583-597.
9. P.G. Dodds, T.K. Dodds and B. de Pagter, Fully symmetric operator spaces, Integr. Equat Oper. Th. 15 (1992), 942-972.
10. T. Fack and H. Kosaki, Generalized s-numbers of τ-measurable operators, Pacific J. Math. 123 (1986), 269-300.
11. I.C. Gohberg and M.G. Krein, Introduction to the theory of non-selfadjoint operators Translations of Mathematical Monographs, vol.18, AMS (1969).
12. D. Guido and T. Isola, Singular traces on semifinite von Neumann algebras, J. Funct. Anal. 134 (1995), 451-485.
13. A. Kaminska, Some remarks on Orlicz-Lorentz spaces, Math. Nachr. 147 (1990) 29-38.
14. S.G. Krein, Ju. I. Petunin and E.M. Semenov, Interpolation of linear operators, Translations of Mathematical Monographs, Amer. Math. Soc. 54 (1982).
15. G.Ya. Lozanovskii, On localizable functionals in vector lattices, in: Theory of Functions, Functional Analysis and their Applications, 19 (1974) 66-80 (Russian).
16. G.Ya. Lozanovskii, On the representation of linear functionals in Marcinkiewicz spaces, Izvestiya VUZov. Matematika N1 (188) (1978) 43-53. (Russian)
17. G.Ya. Lozanovskii, A supplement to the paper "On localizable functionals in vector lattices", J. Soviet Math. 14 (1980), 1170-1173.
18. E. Nelson, Notes on non-commutative integration, J. Functional Anal. 15 (1974), 103-116.
19. R. Prinzis, Traces Residuelles et Asymptotique du Spectre d'Operateurs Pseudo-Differentiels, Ph.D. Thesis, Lyon, 1995.
20. G.Russu, Symmetric spaces not having the majorant property, Mat. Issled. 4 (1969), 82-93 (Russian).
21. ∞} but which is not a subspace of any interpolation space, in Studies in the theory of functions of many real variables, Collection of papers, Yaroslavl (1990), (134-139).
22. K. Sundaresan, Additive functionals on Orlicz spaces, Studia Math. 32 (1969), 269-276.
23. p-spaces associated with von Neumann algebras, Notes, Copenhagen Univ. (1981).
24. J.V. Varga, Traces on irregular ideals, Proc. Amer. Math. Soc. 107 (1989) 715-723.
25. A.C. Zaanen, Riesz Spaces II, (North-Holland), Amsterdam-New York-Oxford (1983).