A characterization of the second dual of

Authors:
Stephen T. L. Choy and James C. S. Wong

Journal:
Proc. Amer. Math. Soc. **120** (1994), 203-211

MSC:
Primary 46E40; Secondary 46G99, 46J10

DOI:
https://doi.org/10.1090/S0002-9939-1994-1163330-1

MathSciNet review:
1163330

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a locally compact Hausdorff space, and let be a Banach space. The space of the continuous functions from to vanishing at infinity is denoted by . Let be the space of the representing measures of all the bounded linear functionals on . For let

**[1]**J. Batt and E.J. Berg,*Linear bounded transformations on the space of continuous functions*, J. Funct. Anal.**4**(1969), 215-239. MR**0248546 (40:1798)****[2]**J. K. Brooks and P. W. Lewis,*Linear operators and vector measures*, Trans. Amer. Math. Soc.**192**(1974), 139-162. MR**0338821 (49:3585)****[3]**M. Cambern and P. Grein,*The bidual of*, Proc. Amer. Math. Soc.**85**(1982), 53-58. MR**647896 (83f:46042)****[4]**S. T. L. Choy,*Positive operators and algebras of dominated measures*, Rev. Roumaine Math. Pures Appl., vol. 34, Ed. Acad. R. S. România, Bucharest, 1989, pp. 213-219. MR**1006639 (90g:47055)****[5]**S. T. L. Choy and J. C. S. Wong,*The second dual of*, J. Austral. Math. Soc. (to appear).**[6]**J. Diestel,*Sequences and series in Banach spaces*, Graduate Texts in Math., vol. 92, Springer-Verlag, New York, 1984. MR**737004 (85i:46020)****[7]**J. Diestel and J. J. Uhl,*Vector measures*, Math. Surveys Monographs, vol. 15, Amer. Math. Soc., Providence, RI, 1977. MR**0453964 (56:12216)****[8]**N. Dinculeanu,*Vector measures*, Pergamon Press, New York, 1967. MR**0206190 (34:6011b)****[9]**J. Duncan and S. A. R. Hosseinium,*The second dual of a Banach algebra*, Proc. Roy. Soc. Edinburgh Sect. A**84**(1979), 309-325. MR**559675 (81f:46057)****[10]**A. I. Tulcea and C. I. Tulcea,*Topics in the theory of lifting*, Springer-Verlag, Heidelberg and New York, 1969. MR**0276438 (43:2185)****[11]**J. C. Wong,*Abstract harmonic analysis of generalized functions on locally compact semi-groups with applications to invariant means*, J. Austral. Math. Soc. Ser. A**23**(1977), 84-94. MR**0438044 (55:10965)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1163330-1

Keywords:
Second dual,
vector-valued function space,
Bochner integrable functions

Article copyright:
© Copyright 1994
American Mathematical Society