Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T16:40:22.119Z Has data issue: false hasContentIssue false

A Note on M-Summands in Dual Spaces

Published online by Cambridge University Press:  20 November 2018

Timothy Feeman*
Affiliation:
Department of Mathematical Sciences Villanova University Villanova, PA 19085
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A theorem concerning M-summands in dual spaces is used to prove that certain known M-ideals are not M-summands. In some cases where this information was already known, our procedure greatly simplifies the earlier proofs. Finally, we give a condition to determine which M-ideals in dual spaces are M-summands and which are not.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Alfsen, Eric M. and Effros, Edward G., Structure in real Banach spaces, Ann. of Math. 96 (1972), pp. 98173.Google Scholar
2. Sheldon, Axler, David Berg, I., Nicholas, Jewell, and Allen, Shields, Approximation by compact operators and the space H∞ + C, Ann. of Math. 109 (1979), pp. 601612.Google Scholar
3. Cunningham, F. Jr., M-structure in Banach Spaces, Proc. Camb. Phil. Soc. 63 (1967), pp. 613629.Google Scholar
4. Cunningham, F. Jr., Effros, E., and Roy, N., M-structure in dual Banach spaces, Israel J. Math. 14(1973), pp. 304309.Google Scholar
5. Dixmier, J., Les fonctionelles linéaires sur l'ensemble des opérateurs bornés d'un espace de Hilbert, Ann. of Math. 51 (1950), pp. 387408.Google Scholar
6. Dunford, N., Schwartz, J., Linear Operators, part 1, Interscience, New York, 1958.Google Scholar
7. Fall, T., Arveson, W., and Muhly, P., Perturbations of nest algebras, J. Operator Theory 1 (1979), pp. 137150.Google Scholar
8. Feeman, Timothy G., M-ideals and quasi-triangular algebras, Illinois J. Math. 31 (1987), pp. 8998.Google Scholar
9. Richard, Holmes, Bruce, Scranton, and Joseph, Ward, Approximation from the space of compact operators and other M-ideals, Duke Math. J. 42 (1975), pp. 259269.Google Scholar
10. Luecking, Daniel H., The compact Hankel operators form an M-ideal in the space of all Hankel operators, Proc. A.M.S. 79 (1980), pp. 222224.Google Scholar
11. Robert, Schatten, Norm ideals of completely continuous operators, Ergebnisse der Math, und ihrer Grenzgebiete 27, Springer-Verlag (1960).Google Scholar
12. Younis, R., Best approximation in certain Douglas algebras, Proc. A.M.S. 80 (1980), pp. 639642.Google Scholar
13. Younis, R., Properties of certain algebras between L∞ and H∞ J. Func. Analysis 44 (1981), pp. 381387.Google Scholar