, Volume 9, Issue 3, pp 485–490 | Cite as

Equicontinuity in Measure Spaces and von Neumann Algebras

  • J. K. BrooksEmail author


Fourier Analysis Operator Theory Measure Space Potential Theory 
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  1. 1.
    Akemann, C.A. 1967The dual space of an operator algebraTrans. Am. Math. Soc.126286302Google Scholar
  2. 2.
    Akemann, C.A., Dodds, P.G., Gamlen, P.G. 1972Weak compactness in the dual space of a \({\mathcal{C}}^{\ast}\)-algebraJ. Funct. Anal.10446450CrossRefGoogle Scholar
  3. 3.
    Brooks, J.K., Jewett, R.S. 1970On finitely additive vector measuresProc. Natl. Acad. Sci.6712941298Google Scholar
  4. 4.
    Brooks, J.K. 1973Equicontinuous sets of measures and applications to Vitali’s integral convergence theorem and control measuresAdv. Math.10165171CrossRefGoogle Scholar
  5. 5.
    Brooks, J.K. 1980On a theorem of DieudonnéAdv. Math.36165168CrossRefGoogle Scholar
  6. 6.
    Brooks, J.K., Chacon, R.V. 1980Continuity and compactness of measuresAdv. Math.371626CrossRefGoogle Scholar
  7. 7.
    Brooks, J.K., Dinculeanu, N. 1977Weak compactness in spaces of Bochner integrable functions and applicationsAdv. Math.24172188CrossRefGoogle Scholar
  8. 8.
    Brooks, J.K., Saitô, K., Wright, J.D.M. 2002A bounded sequence of normal functionals has a subsequence which is nearly weakly convergentJ. Math. Anal. Appl.276160167CrossRefGoogle Scholar
  9. 9.
    Brooks, J.K., Saitô, K., Wright, J.D.M. 2003Operator algebras and a theorem of DieudonnéRendi. Circ. Mat. Palermo52514Google Scholar
  10. 10.
    Brooks, J.K., Saitô, K. and Wright, J.D.M.: When absolute continuity on \({\mathcal{C}}^{\ast}\)-algebras is automatically uniform, Oxford Quart. J. Math. (in press).Google Scholar
  11. 11.
    Brooks, J.K., Wright, J.D.M. 2001Representing Yosida–Hewitt decompositions for classical and non-commutative vector measuresExpo. Math.19373383CrossRefGoogle Scholar
  12. 12.
    Brooks, J.K., Wright, J.D.M. 2001Convergence in the dual of a σ-complete \({\mathcal{C}}^{\ast}\)-algebraJ. Math. Anal. Appl.294141146CrossRefGoogle Scholar
  13. 13.
    Dunford, N., Schwartz, J.T. 1958Linear OperatorsInterscienceNew Yorkvol. IGoogle Scholar
  14. 14.
    Kadison, R.V. and Ringrose, J.R.: Fundamentals of the Theory of Operator Algebras vol. I and vol. II. Academic Press, London–Orlando, 1983 and 1986.Google Scholar
  15. 15.
    Pedersen, G.K. 1979\({\mathcal{C}}^{\ast}\)-Algebras and their Automorphism GroupsAcademic PressLondon–New YorkGoogle Scholar
  16. 16.
    Pfitzner, H. 1994Weak compactness in the dual of a \({\mathcal{C}}^{\ast}\)-algebra is determined commutativelyMath. Ann.298349371CrossRefGoogle Scholar
  17. 17.
    Saitô, K. 1967On the preduals of \({\mathcal{W}}^{\ast}\)-algebrasTôhoku Math. J.19324331Google Scholar
  18. 18.
    Saitô, K., Wright, J.D.M. 2003\({\mathcal{C}}^{\ast}\)-algebras which are Grothendieck spacesRendi. Circ. Mat. Palermo52141144Google Scholar
  19. 19.
    Takesaki, M. 1958On the conjugate space of an operator algebraTôhoku Math. J.10194203Google Scholar
  20. 20.
    Takesaki, M.: Theory of Operator Algebras I. New York–Heidelberg–Berlin, 1979.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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