Skip to main content
    • Aa
    • Aa

Weakly compact subsets of symmetric operator spaces

  • Peter G. Dodds (a1), Theresa K. Dodds (a1) and Ben De Pagter (a2)

Under natural conditions it is shown that the rearrangement invariant hull of a weakly compact subset of a properly symmetric Banach space of measurable operators affiliated with a semi-finite von Neumann algebra is again relatively weakly compact.

Hide All
[1]Aliprantis C. D. and Burkinshaw O.. Positive Operators (Academic Press, 1985).
[2]Akemann C. A.. The dual space of an operator algebra. Trans. Amer. Math. Soc. 126 (1967), 286302.
[3]Ando T.. On fundamental properties of a Banach space with a cone. Pacific J. Math. 12 (1962), 11631169.
[4]Chong K. M.. Spectral orders, uniform integrability and Lebesgue's dominated convergence theorem. Trans. Amer. Math. Soc. 191 (1974), 395404.
[5]Dodds P. G., Dodds T. K. and Pagter B. de. Non-commutative Banach function spaces. Math. Z. 201 (1989), 583597.
[6]Dodds P. G., Dodds T. K. and Pagter B. de. A general Markus inequality. Proc. CMA (ANU), Miniconference on Operators in Analysis 24 (1989), 4757.
[7]Dodds P. G., Dodds T. K. and Pagter B. de. Non-commutative Köthe duality. TU Delft (1990).
[8]Diestel J.. Sequences and Series in Banach Space. Graduate Texts in Math. no. 92 (Springer-Verlag, 1984).
[9]Dodds P. G. and Lennard C. J.. Normality in trace ideals. J. Operator Theory 16 (1986), 127145.
[10]Dunford N. and Schwartz J.. Linear Operators, Part I (Wiley-Interscience, 1964).
[11]Fack T. and Kosaki H.. Generalized s-numbers of τ-measurable operators. Pacific J. Math. 123 (1986), 269300.
[12]Fremlin D. H.. Topological Riesz Spaces and Measure Theory (Cambridge University Press, 1974).
[13]Fremlin D. H.. Stable subspaces of L 1+L . Proc. Cambridge Philos. Soc. 64 (1968), 625643.
[14]Garling D. J. H.. On symmetric sequence spaces. Proc. London Math. Soc. 16 (1966), 85106.
[15]Garling D. J. H.. On ideals of operators in Hilbert space. Proc. London Math. Soc. 17 (1967), 115138.
[16]Grothendieck A.. Topological Vector Spaces (Gordon and Breach, 1973).
[17]Krein S. G., Petunin Ju. I. and Semenov E. M.. Interpolation of linear operators. Translations of Mathematical Monographs. Amer. Math. Soc. 54 (1982).
[18]Luxemburg W. A. J.. Rearrangement invariant Banach function spaces. Queen's Papers in Pure and Appl. Math. no. 10 (1967), 83144.
[19]Nelson E.. Notes on non-commutative integration. J. Fund. Anal. 15 (1974), 103116.
[20]Ovčinnikov V. I.. s-numbers of measurable operators. Funktsional. Anal. i Prilozhen. 4 (1970), 7885.
[21]Ovčinnikov V. I.. Symmetric spaces of measurable operators. Dokl. Akad. Nauk SSSR 191 (1970), 769771 (Russian)
Ovčinnikov V. I.. English Translation: Soviet Math. Dokl. 11 (1970), 448451.
[22]Ryff J. V.. Orbits of L 1-functions under doubly stochastic transformations. Trans. Amer. Math. Soc. 117 (1965), 92100.
[23]Sakai S.. Topological properties of W*-algebras. Proc. Japan Acad. 33 (1957), 439444.
[24]Sukochew F.. Construction of non-commutative symmetric spaces. Dokl. Akad. Nauk UzSSR 8 (1986), 46.
[25]Takesaki M.. Theory of Operator Algebras I (Springer-Verlag, 1979).
[26]Terp M.. L p-spaces associated with von Neumann algebras. Notes, Copenhagen University, (1981).
[27]Yeadon F. J.. Ergodic theorems for semifinite von Neumann algebras: II. Math. Proc. Cambridge Philos. Soc. 88 (1980), 135147.
[28]Zaanen A. C.. Integration (North-Holland, 1967).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 8 *
Loading metrics...

Abstract views

Total abstract views: 38 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th October 2017. This data will be updated every 24 hours.