Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T01:30:18.240Z Has data issue: false hasContentIssue false
  • English
  • Français

The M-ideal structure of some algebras of bounded linear operators

Published online by Cambridge University Press:  14 November 2011

Nigel J. Kalton  and
Dirk Werner
Nigel J. Kalton
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211U.S.A., e-mail: [email protected]
Dirk Werner
Affiliation:
I. Mathematisches Institut, Freie Universität Berlin, Arnimallee 2–6, 14195 Berlin, Germany, e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

Let 1 < p, q < ∞. It is shown for complex scalars that there are no nontrivial M-ideals in ℒ(Lp[0, 1]) if p ≠ 2, and is the only nontrivial M-ideal in .

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 3 , 1995 , pp. 493 - 500
Copyright
Copyright © Royal Society of Edinburgh 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Alfsen, E. M. and Effros, E. G.. Structure in real Banach spaces. Part I and II. Ann. of Math. 96 (1972), 98–173.CrossRefGoogle Scholar
2Alspach, D.. Small into isomorphisms on Lp spaces. Illinois J. Math. 27 (1983), 300–14.CrossRefGoogle Scholar
3Behrends, E.. On the geometry of spaces of C0K-valued operators. Studia Math. 90 (1988), 135–51.CrossRefGoogle Scholar
4Bonsall, F. F. and Duncan, J.. Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Mathematical Society Lecture Note Series 2 (Cambridge: Cambridge University Press, 1971).CrossRefGoogle Scholar
5Bonsall, F. F. and Duncan, J.. Numerical Ranges II, London Mathematical Society Lecture Note Series 10 (Cambridge: Cambridge University Press, 1973).CrossRefGoogle Scholar
6Casazza, P. G., Kottman, C. A. and Lin, B.-L.. On some classes of primary Banach spaces. Canad. J. Math. 29 (1977), 856–73.CrossRefGoogle Scholar
7Cho, C.-M. and Johnson, W. B.. A characterization of subspaces X of lp for which K(X) is an M-ideal in L(X). Proc. Amer. Math. Soc. 93 (1985), 466–70.Google Scholar
8Cho, C.-M. and Johnson, W. B.. M-ideals and ideals in L(X). J. Operator Theory 16 (1986), 245–60.Google Scholar
9Flinn, P. H.. A characterization of M-ideals in B(l p) for 1 < p < ∞. Pacific J. Math. 98 (1982), 73–80.CrossRefGoogle Scholar
10Godefroy, G., Kalton, N. J. and Saphar, P. D.. Unconditional ideals in Banach spaces. Studia Math. 104 (1993), 13–59.CrossRefGoogle Scholar
11Harmand, P. and Lima, Å.. Banach spaces which are M-ideals in their biduals. Trans. Amer. Math. Soc. 283 (1984), 253–64.Google Scholar
12Harmand, P., Werner, D. and Werner, W.. M-ideals in Banach Spaces and Banach Algebras, Lecture Notes in Mathematics 1547 (Berlin: Springer, 1993).CrossRefGoogle Scholar
13Kalton, N. J.. M-ideals of compact operators. Illinois J. Math. 37 (1993), 147–69.CrossRefGoogle Scholar
14Lima, Å.. M-ideals of compact operators in classical Banach spaces. Math. Scand. 44 (1979), 207–17.CrossRefGoogle Scholar
15Lindenstrauss, J. and Tzafriri, L.. Classical Banach Spaces I (Berlin: Springer, 1977).CrossRefGoogle Scholar
16Oja, E.. Dual de l'espace des opérateurs linéaires continus. C. R. Acad. Sci. Paris, Sér. A 309 (1989), 983–6.Google Scholar
17Oja, E. and Werner, D.. Remarks on M-ideals of compact operators on X⊕pX. Math. Nachr. 152 (1991), 101–11.CrossRefGoogle Scholar
18Payá, R. and Werner, W.. An approximation property related to M-ideals of compact operators. Proc. Amer. Math. Soc. 111 (1991), 993–1001.CrossRefGoogle Scholar
19Royden, H. L.. Real Analysis 2nd edn (New York: Macmillan, 1968).Google Scholar
20Smith, R. R. and Ward, J. D.. M-ideal structure in Banach algebras. J. Funct. Anal. 27 (1978), 337–49.CrossRefGoogle Scholar
21Smith, R. R. and Ward, J. D.. Applications of convexity and M-ideal theory to quotient Banach algebras. Quart. J. Math. Oxford (2) 30 (1979), 365–84.CrossRefGoogle Scholar
22Werner, D.. Remarks on M-ideals of compact operators. Quart. J. Math. Oxford (2) 41 (1990), 501–7.CrossRefGoogle Scholar
23Werner, D.. M-ideals and the ‘basic inequality’. J. Approx. Theory 76 (1994), 21–30.CrossRefGoogle Scholar
24Werner, W.. Inner M-ideals in Banach space algebras. Math. Ann. 291 (1991), 205–23.CrossRefGoogle Scholar