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A Note on M-Summands in Dual Spaces

Published online by Cambridge University Press:  20 November 2018

Timothy Feeman
Timothy Feeman*
Affiliation:
Department of Mathematical Sciences Villanova University Villanova, PA 19085
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Abstract

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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.

Keywords

Primary 46B10Secondary 47D2541A50M-summandM-ideal
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 393 - 398
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. 98–173.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. 601–612.Google Scholar
3. Cunningham, F. Jr., M-structure in Banach Spaces, Proc. Camb. Phil. Soc. 63 (1967), pp. 613–629.Google Scholar
4. Cunningham, F. Jr., Effros, E., and Roy, N., M-structure in dual Banach spaces, Israel J. Math. 14(1973), pp. 304–309.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. 387–408.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. 137–150.Google Scholar
8. Feeman, Timothy G., M-ideals and quasi-triangular algebras, Illinois J. Math. 31 (1987), pp. 89–98.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. 259–269.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. 222–224.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. 639–642.Google Scholar
13. Younis, R., Properties of certain algebras between L∞ and H∞ J. Func. Analysis 44 (1981), pp. 381–387.Google Scholar