A note concerning

Author:
H. Elton Lacey

Journal:
Proc. Amer. Math. Soc. **29** (1971), 525-528

MSC:
Primary 46.10

MathSciNet review:
0278040

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that there are exactly two abstract *L*-spaces which are duals of infinite dimensional separable Banach spaces.

**[1]**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**0625855**, 10.1090/S0002-9939-1969-0625855-X**[2]**A. J. Lazar and J. Lindenstrass,*Banach spaces whose duals are L spaces and their representing matrices*, Acta. Math. (to appear).**[3]**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) Princeton Univ. Press, Princeton, N. J., 1972, pp. 235–273. Ann. of Math. Studies, No. 69. MR**0417761****[4]**Dorothy Maharam,*On homogeneous measure algebras*, Proc. Nat. Acad. Sci. U. S. A.**28**(1942), 108–111. MR**0006595****[5]**R. Nirenberg and R. Panzone,*On the spaces 𝐿¹ which are isomorphic to a 𝐵**, Rev. Un. Mat. Argentina**21**(1963), 119–130 (1963). MR**0167823****[6]**A. Pełczyński,*On Banach spaces containing 𝐿₁(𝜇)*, Studia Math.**30**(1968), 231–246. MR**0232195****[7]**Robert R. Phelps,*Lectures on Choquet’s theorem*, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR**0193470****[8]**Haskell P. Rosenthal,*On injective Banach spaces and the spaces 𝐿^{∞}(𝜇) for finite measure 𝜇*, Acta Math.**124**(1970), 205–248. MR**0257721****[9]**Haskell P. Rosenthal,*On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from 𝐿^{𝑝}(𝜇) to 𝐿^{𝑟}(𝜈)*, J. Functional Analysis**4**(1969), 176–214. MR**0250036**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0278040-7

Keywords:
*L*-space,
dual *L*-space,
spaces whose duals are *L*-spaces

Article copyright:
© Copyright 1971
American Mathematical Society