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InnerM-ideals in Banach algebras

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References

  1. Alfsen, E.M., Effros, E.G.: Structure in real Banach spaces. Part I and II. Ann. Math.96(2), 98–173 (1972)

    Google Scholar 

  2. Axler, S., Jewell, N., Shields, A.: The essential numerical range of an operator and its adjoint. Trans. Am. Math. Soc.261, 159–167 (1980)

    Google Scholar 

  3. Behrends, E.:M-Structure and the Banach-Stone theorem. (Lect. Notes Math., vol. 736) Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  4. Behrends, E.: Multiplier representations and an application to the problem whetherA⊗ɛ X determinesA and/orX. Math. Scand.52, 117–144 (1983)

    Google Scholar 

  5. Behrends, E.: Normal operators and multipliers on complex Banach spaces and a symmetry property ofL 1-predual spaces. Isr. J. Math.47, 23–28 (1984)

    Google Scholar 

  6. Behrends, E.: Sur lesM-idéaux des espaces d'opérateurs compacts. In: Beauzamy, B., Maurey, B., Pisier, G. (eds.) Séminaire d'Analyse Fonctionnelle 1984/85. (Publ. Math. Univ. Paris VI/VII, pp. 11–18) Paris 1985

  7. Behrends, E.: A generalization of the principle of local reflexivity. Rev. Roum. Math. Pures Appl.31, 293–296 (1986)

    Google Scholar 

  8. Behrends, E.: On the geometry of spaces ofC 0 K-valued operators. Studia Math.90, 135–151 (1988)

    Google Scholar 

  9. Behrends, E., Danckwerts, R., Evans, R., Göbel, S., Greim, P., Meyfarth, K., Müller, W.:L p-Structure in real Banach spaces (Lect. Notes Math., vol. 613) Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  10. Behrends, E., Harmand, P.: Banach spaces which are properM-ideals. Studia Math.81, 159–169 (1985)

    Google Scholar 

  11. Behrends, E., Wodinski, G.: A note on hermitian operators on complex Banach spaces. Bull. Pol. Acad. Sci.35, 801–803 (1987)

    Google Scholar 

  12. Bonsall, F.F., Duncan, J.: Numerical ranges of operators on normed spaces and of elements of normed algebras. (Lond. Math. Soc. Lect. Note Ser., vol. 2) Cambridge: Cambridge University Press 1971

    Google Scholar 

  13. Bonsall, F.F., Duncan, J.: Complete normed algebras. Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  14. Bonsall, F.F., Duncan, J.: Numerical ranges. II. (Lond. Math. Soc. Lect. Note Ser., vol. 10) Cambridge: Cambridge University Press 1973

    Google Scholar 

  15. Cho, C.-M., Johnson, W.B.: A characterization of subspacesX of ℓp for whichK(X) is anM-ideal inL(X). Proc. Am. Math. Soc.93, 466–470 (1985)

    Google Scholar 

  16. Cho, C.-M., Johnson, W.B.:M-ideals and ideals inL(X). J. Oper. Theory16, 245–260 (1986)

    Google Scholar 

  17. Chui, C.K., Legg, D.A., Smith, P.W., Ward, J.D.: On a question of Olsen concerning compact perturbations of operators. Mich. Math. J.24, 119–127 (1977)

    Google Scholar 

  18. Chui, C.K., Smith, P.W., Smith, R.R., Ward, J.D.:L-ideals and numerical range preservation. II. J. Math.21, 365–373 (1977)

    Google Scholar 

  19. Civin, P., Yood, B.: The second conjugate space of a Banach algebra as an algebra. Pac. J. Math.11, 847–870 (1961)

    Google Scholar 

  20. Dineen, S., Klimek, M., Timoney, R.M.: Biholomorphic mappings and banach function modules. J. Reine Angew. Math.387, 122–147 (1988)

    Google Scholar 

  21. Duncan, J., Hosseiniun, S.A.R.: The second dual of a Banach algebra. Proc. R. Soc. Edinb.84, 309–325 (1979)

    Google Scholar 

  22. Dunford, N., Schwartz, J.T.: Linear operators. Part 1: General theory. New York: Interscience Publishers 1958

    Google Scholar 

  23. Fabian, M., Godefroy, G.: The dual of every Asplund space admits a projectional resolution of the identity. Studia Math.91, 141–151 (1988)

    Google Scholar 

  24. Fakhoury, H.: Approximation par des opérateurs compacts ou faiblement compact à valeurs dansC(X). Ann. Inst. Fourier27(4), 147–167 (1977)

    Google Scholar 

  25. Fakhoury, H.: Sur lesM-idéaux dans certains espaces d'opérateurs et l'approximation par des opérateurs compacts. Can. Math. Bull.23, 401–411 (1980)

    Google Scholar 

  26. Flinn, P.H., Smith, R.R.:M-structure in the Banach algebra of operators onC 0(Ω). Trans. Am. Math. Soc.281, 233–242 (1984)

    Google Scholar 

  27. Gamelin, T.W.: Uniform algebras. Englewood Cliffs: Prentice-Hall 1969

    Google Scholar 

  28. Godefroy, G., Iochum, B.: Arens-regularity of Banach algebras and the geometry of Banach spaces. J. Funct. Anal.80, 47–59 (1988)

    Google Scholar 

  29. Godefroy, G., Saab, P.: Weakly unconditionally convergent series inM-ideals. Math. Scand.64, 307–318 (1989)

    Google Scholar 

  30. Godefroy, G., Saphar, P.: Duality in spaces of operators and smooth norms on Banach spaces. III. J. Math.32, 672–695 (1983)

    Google Scholar 

  31. Harmand, P., Lima, Å.: Banach spaces which areM-ideals in their biduals. Trans. Am. Math. Soc.283, 253–264 (1983)

    Google Scholar 

  32. Harmand, P., Werner, D., Werner, W.:M-ideals in Banach spaces and Banach algebras. (In preparation)

  33. Hirsberg, B.:M-ideals in complex function spaces and algebras. Isr. J. Math.12, 133–146 (1972)

    Google Scholar 

  34. Holmes, R.B.:M-ideals in approximation theory. In: Lorentz, G.G., Chui, C.K., Schumaker, L.L. (eds.) Approximation theory. II. Proc. Int. Symp., pp. 391–396. Austin 1976. New York: Academic Press 1976

    Google Scholar 

  35. Holmes, R.B., Kripke, B.R.: Best approximation by compact operators. Indiana Univ. Math. J.21, 255–263 (1971)

    Google Scholar 

  36. Holmes, R.B., Scranton, B., Ward, J.: Best approximation by compact operators. II. Bull. Am. Math. Soc.80, 98–102 (1974)

    Google Scholar 

  37. Holmes, R.B., Scranton, B., Ward, J.: Approximation from the space of compact operators and otherM-ideals. Duke Math. J.42, 259–269 (1975)

    Google Scholar 

  38. Johnson, B.E.: Banach Algebras: Introductory course. In: Williamson, J.H. (ed.) Algebras in analysis, pp. 63–83. London: Academic Press 1975

    Google Scholar 

  39. Li, D.: Quantitative unconditionality of Banach spacesE for whichK(E) is anM-ideal inL(E). Studia Math.96, 39–50 (1990)

    Google Scholar 

  40. Lima, Å.: Intersection properties of balls and subspaces in Banach spaces. Trans. Am. Math. Soc.227, 1–62 (1977)

    Google Scholar 

  41. Lima, Å.: OnM-ideals and best approximation. Indiana Univ. Math. J.31, 27–36 (1982)

    Google Scholar 

  42. Lindenstrauss, J., Rosenthal, H.P.: The ℒ p spaces. Isr. J. Math.7, 325–349 (1969)

    Google Scholar 

  43. Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces. I. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  44. Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces. II. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  45. Mach, J., Ward, J.D.: Approximation by compact operators on certain Banach spaces. J. Approximation Theory23, 274–286 (1978)

    Google Scholar 

  46. Oja, E., Werner, D.: Remarks onM-ideals of compact opX⊕ p X. Math. Nachr.152, 101–111 (1991)

    Google Scholar 

  47. Palmer, T.W.: The bidual of the compact operators. Trans. Am. Math. Soc.288, 827–839 (1985)

    Google Scholar 

  48. Partington, J.R.: Hermitian operators for absolute norms and absolute direct sums. Linear Algebra Appl.23, 275–280 (1979)

    Google Scholar 

  49. Payá, R., Werner, W.: An approximation property related toM-ideals of compact operators. Proc. Am. Math. Soc.111, 993–1001 (1991)

    Google Scholar 

  50. Payá-Albert, R., Pérez, J., Rodríguez-Palacios, A.: Noncommutative JordanC *-algebras. Manuscr. Math.37, 87–120 (1982)

    Google Scholar 

  51. Saatkamp, K.:M-ideals of compact operators. Math. Z.158, 253–263 (1978)

    Google Scholar 

  52. Saatkamp, K.: Best approximation in the space of bounded operators and its applications. Math. Ann.250, 35–54 (1980)

    Google Scholar 

  53. Smith, R.R.: An addendum to “M-ideal structure in Banach algebras”. J. Funct. Anal.32, 269–271 (1979)

    Google Scholar 

  54. Smith, R.R., Ward, J.D.:M-ideal structure in Banach algebras. J. Funct. Anal.27, 337–349 (1978)

    Google Scholar 

  55. Smith, R.R., Ward, J.D.: Applications of convexity andM-ideal theory to quotient Banach algebras. Q. J. Math., Oxf. II. Ser.30, 365–384 (1979)

    Google Scholar 

  56. Stout, E.L.: The theory of uniform algebras. Tarrytown-on-Hudson: Bogden & Quigley 1971

    Google Scholar 

  57. Werner, D.: Remarks onM-ideals of compact operators. Q. J. Math., Oxf. II. Ser.41, 501–507 (1990)

    Google Scholar 

  58. Werner, D., Werner, W.: On theM-structure of the operator spaceL(CK). Studia Math.87, 133–138 (1987)

    Google Scholar 

  59. Werner, W.: On theM-structure of spaces of bounded operators and Banach algebras. Dissertation, FU Berlin, 1988

  60. Werner, W.: Some results concerning theM-structure of operator spaces. Math. Ann.282, 545–553 (1988)

    Google Scholar 

  61. Werner, W.: Characterizing the asymptotic behaviour of the MAP on subspaces ofc 0. (Preprint 1990)

  62. Wodinski, G.: Multiplikatoren in komplexen Banachräumen. Dissertation, FU Berlin, 1986

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Werner, W. InnerM-ideals in Banach algebras. Math. Ann. 291, 205–223 (1991). https://doi.org/10.1007/BF01445200

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