On properties of subspaces of $l_{p}, 0<p<1$
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- by W. J. Stiles PDF
- Trans. Amer. Math. Soc. 149 (1970), 405-415 Request permission
Abstract:
The material presented in this paper deals with some questions concerning projections, quotient spaces, and linear dimension in ${l_p}$ spaces, and also includes a remark about weak Schauder bases in ${l_p}$ spaces and an example of an infinite-dimensional closed subspace of ${l_p}$ which is not isomorphic to ${l_p}$.References
- Tosio Aoki, Locally bounded linear topological spaces, Proc. Imp. Acad. Tokyo 18 (1942), 588–594. MR 14182 S. Banach, Théorie des opérations linéaires, Monografie Mat. PWN, Warsaw, 1932; reprint, Chelsea, New York, 1955. MR 17, 175.
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
- M. I. Kadec and A. Pełczyński, Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$, Studia Math. 21 (1961/62), 161–176. MR 152879, DOI 10.4064/sm-21-2-161-176
- Joram Lindenstrauss, On some subspaces of $l^{1}$ and $c_{0}$, Bull. Res. Council Israel Sect. F 10F (1961), 74–80. MR 187059
- J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in $L_{p}$-spaces and their applications, Studia Math. 29 (1968), 275–326. MR 231188, DOI 10.4064/sm-29-3-275-326
- Joram Lindenstrauss, On complemented subspaces of $m$, Israel J. Math. 5 (1967), 153–156. MR 222616, DOI 10.1007/BF02771101
- R. E. A. C. Paley, Some theorems on abstract spaces, Bull. Amer. Math. Soc. 42 (1936), no. 4, 235–240. MR 1563277, DOI 10.1090/S0002-9904-1936-06277-4
- A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209–228. MR 126145, DOI 10.4064/sm-19-2-209-228
- S. Rolewicz, On a certain class of linear metric spaces, Bull. Acad. Polon. Sci. Cl. III. 5 (1957), 471–473, XL (English, with Russian summary). MR 0088682
- H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555
- R. J. Whitley, Strictly singular operators and their conjugates, Trans. Amer. Math. Soc. 113 (1964), 252–261. MR 177302, DOI 10.1090/S0002-9947-1964-0177302-2
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 149 (1970), 405-415
- MSC: Primary 46.01
- DOI: https://doi.org/10.1090/S0002-9947-1970-0261315-9
- MathSciNet review: 0261315