Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T04:14:54.087Z Has data issue: false hasContentIssue false
  • English
  • Français

On Some Classes of Primary Banach Spaces

Published online by Cambridge University Press:  20 November 2018

P. G. Casazza ,
C. A. Kottman  and
Bor-Luh Lin
P. G. Casazza
Affiliation:
The University of Alabama in Huntsville, Huntsville, Alabama
C. A. Kottman
Affiliation:
Oregon State University, Corvallis, Oregon
Bor-Luh Lin
Affiliation:
The University of Iowa, Iowa City, Iowa
Rights & Permissions [Opens in a new window]

Extract

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 Banach space X is called primary (respectively, prime) if for every (bounded linear) projection P on X either PX or (I — P)X (respectively, PX with dim PX = ∞ ) is isomorphic to X. It is well-known that C0 and lp, 1 ≦ p ≦ ∞ [8; 14] are prime. However, it is unknown whether there are other prime Banach spaces. For a discussion on prime and primary Banach spaces, we refer the reader to [9].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 856 - 873
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Alspach, D. and Benyamini, Y.. On the primariness of spaces of continuous functions on ordinals, Notices Amer. Math. Soc. 23 (1976), 731–46-27.Google Scholar
2. Alspach, D., Enflo, P. and Odell, E., On the structure of separable f£v spaces (1 < p < ∞), to appear, Studia Math.Google Scholar
3. Bessaga, C. and Pelczynski, A., On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164.Google Scholar
4. Bessaga, C. and Pelczynski, A. A generalization of results of R. C. James concerning absolute bases in Banach spaces, Studia Math. 17 (1958), 165–174.Google Scholar
5. Casazza, P. G. and Lin, B. L., Projections on Banach spaces with symmetric bases, Studia Math. 52 (1975), 189–193.Google Scholar
6. Casazza, P. G., Kottman, C. A. and Lin, B. L., On primary Banach spaces, Bull. Amer. Math. Soc, 82 (1976), 71–73.Google Scholar
7. Edelstein, I. and Mityagin, B. S., Homogopy type of linear groups of two classes of Banach spaces, Functional Analysis and its Appl. 4 (1970), 221–231.Google Scholar
8. Lindenstrauss, J., On complemented subspaces of m, Israel J. Math. 5 (1967), 153–156.Google Scholar
9. Lindenstrauss, J. Decompositions of Banach spaces, Indiana Univ. Math. J. 20 (1971), 917–919.Google Scholar
10. Lindenstrauss, J. and Pelczynski, A., Contributions to the theory of the classical Banach spaces, J. Functional Analysis 8 (1971), 225–249.Google Scholar
11. Lindenstrauss, J. and Tzafriri, L., On Orlicz sequence spaces II, Israel J. Math. 11 (1972), 355–379.Google Scholar
12. Lindenstrauss, J. and Tzafriri, L. Classical Banach spaces, Lecture Notes in Math. 338 (Springer-Verlag, 1973).Google Scholar
13. Odell, E., On complemented subspaces of ( £ l2)ipi Israel J. Math. 23 (1976), 353–367.Google Scholar
14. Pelczynski, A., Projections in certain Banach spaces, Studia Math. 19 (1960), 209–228.Google Scholar
15. Rosenthal, H. P., On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36.Google Scholar
16. Rosenthal, H. P., A characterization of Banach spaces containing ll, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413.Google Scholar
17. Ryser, H. J., Combinatorial mathematics, The Carus Mathematical Monographs (Math. Assoc. Amer., 1963).Google Scholar
18. Schechtman, G., Complemented subspaces of (h® h®.. .)P (1 < p < °°) with an unconditional basis, Israel J. Math. 20 (1975), 351–358.Google Scholar
19. Singer, I., Bases in Banach spaces I (Springer-Verlag, 1970).Google Scholar
20. Billard, P., Sur la primante des espaces C([l, a]), C.R. Acad. Sci. Paris 281 (1975), 629–631.Google Scholar