The Mackey topology and complemented subspaces of Lorentz sequence spaces $d(w,p)$ for $0<p<1$
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- by M. Nawrocki and A. Ortyński PDF
- Trans. Amer. Math. Soc. 287 (1985), 713-722 Request permission
Abstract:
In this paper we continue the study of Lorentz sequence spaces $d(w,p)$, $0 < p < 1$, initiated by N. Popa [8]. First we show that the Mackey completion of $d(w,p)$ is equal to $d(v,1)$ for some sequence $v$. Next, we prove that if $d(w,p) \not \subset {l_1}$, then it contains a complemented subspace isomorphic to ${l_p}$. Finally we show that if $\lim {n^{ - 1}}\left (\sum \nolimits _{i = 1}^n {w_i}\right )^{1/p} = \infty$, then every complemented subspace of $d(w,p)$ with symmetric bases is isomorphic to $d(w,p)$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 287 (1985), 713-722
- MSC: Primary 46A45; Secondary 46A10
- DOI: https://doi.org/10.1090/S0002-9947-1985-0768736-7
- MathSciNet review: 768736