A note concerning $A^{\ast } =L_{1} (\mu )$
HTML articles powered by AMS MathViewer
- by H. Elton Lacey PDF
- Proc. Amer. Math. Soc. 29 (1971), 525-528 Request permission
Abstract:
It is shown that there are exactly two abstract L-spaces which are duals of infinite dimensional separable Banach spaces.References
- H. Elton Lacey and Peter D. Morris, On spaces of type $A(K)$ and their duals, Proc. Amer. Math. Soc. 23 (1969), 151–157. MR 625855, DOI 10.1090/S0002-9939-1969-0625855-X A. J. Lazar and J. Lindenstrass, Banach spaces whose duals are L spaces and their representing matrices, Acta. Math. (to appear).
- Joram Lindenstrauss, Weakly compact sets—their topological properties and the Banach spaces they generate, Symposium on Infinite-Dimensional Topology (Louisiana State Univ., Baton Rouge, La., 1967) Ann. of Math. Studies, No. 69, Princeton Univ. Press, Princeton, N. J., 1972, pp. 235–273. MR 0417761
- Dorothy Maharam, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108–111. MR 6595, DOI 10.1073/pnas.28.3.108
- R. Nirenberg and R. Panzone, On the spaces $L^{1}$ which are isomorphic to a $B^{\ast }$, Rev. Un. Mat. Argentina 21 (1963), 119–130 (1963). MR 167823
- A. Pełczyński, On Banach spaces containing $L_{1}(\mu )$, Studia Math. 30 (1968), 231–246. MR 232195, DOI 10.4064/sm-30-2-231-246
- Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
- Haskell P. Rosenthal, On injective Banach spaces and the spaces $L^{\infty }(\mu )$ for finite measure $\mu$, Acta Math. 124 (1970), 205–248. MR 257721, DOI 10.1007/BF02394572
- Haskell P. Rosenthal, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from $L^{p}\,(\mu )$ to $L^{r}\,(\nu )$, J. Functional Analysis 4 (1969), 176–214. MR 0250036, DOI 10.1016/0022-1236(69)90011-1
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 525-528
- MSC: Primary 46.10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0278040-7
- MathSciNet review: 0278040