Abstract
In this paper we study the problems of existence of noncomplemented subspaces and Lozinsky-Kharshilade systems [10] in Banach spaces not isomorphic to Hilbert spaces.
Similar content being viewed by others
References
S. Banach,Théorie des Operations Lineaires, Warsaw, 1932.
F. Bohnenblust,Subspaces of l pn spaces, Amer. J. Math.63 (1941) 64–72.
M. M. Day,On the basis problem in normed spaces, Proc. A.M.S.13 (1962) 655–658.
N. Dunford, and J. Schwartz,Linear Operators (part 1), New York, 1957.
A. Dvoretzky,A characterization of Banach spaces isomorphic to inner product spaces Proc. Coll. Convexity, Univ. of Copenhagen, 1966, 61–66.
C. Foias, and I. Singer:On bases in C([0,1])and L 1([0,1]), Rev. roum. math. pures et appl.,10 (1965) 931–960.
B. Grünbaum,Some applications of expansion constants, Pac. J. Math.10 (1960) 193–201.
R. C. James,Bases and reflexivity of Banach spaces, Ann. Math. (2)52 (1950) 518–527.
J. T. Joichi,Normed linear spaces equivalent to inner product spaces, Proc. A.M.S.,17 (1966) 423–426.
M. I. Kadec,On the systems of Lozynski and Kharshiladze, (Russian), Uspekhi Mat. Nauk18 (1963) No. 5 (113) 167–169.
J. Lindenstrauss,On some subspaces of l 0 and c1, Bull. Res. Council Israel,10F (1961) 74–80.
E. Michael, and A. Pelczynski,Separable Banach spaces which admit l ∞n approximations,Israel J. Math.,4 (1966) 189–198.
F. J. Murray,On complementary manifolds and projections in spaces L p and lp, Trans. Amer. Math. Soc. 41 (1937) 138–152.
I. P. Natanson,Constructive Function Theory, vol. 3,
V. N. Nikolskii,Some problems of best approximation in function space, (Russian), Trudy fiz. mat. fak. Kalininsk. gos. ped. inst.,16 (1954) 119–160.
A. Pelczynski,Some problems on bases in Banach and Frechet spaces, Israel J. Math.2 (1964) 132–138.
A. Sobczyk,Projections in Minkowski and Banach spaces, Duke Math. J.8 (1941) 78–106.
M. Zippin,On a certain basis in c 0, Israel. J. Math.4 (1966) 199–204.
Author information
Authors and Affiliations
Additional information
Supported by N.S.F. Grant number GP-6152
Supported by N.S.F. Grant number GP-2242
Rights and permissions
About this article
Cite this article
Davis, W.J., Dean, D.W. & Singer, I. Complemented subspaces and Λ systems in banach spaces. Israel J. Math. 6, 303–309 (1968). https://doi.org/10.1007/BF02760262
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02760262