Invariant means and cones with vector interiors

Author:
R. J. Silverman

Journal:
Trans. Amer. Math. Soc. **88** (1958), 75-79

MSC:
Primary 46.00

DOI:
https://doi.org/10.1090/S0002-9947-1958-0095414-6

Addendum:
Trans. Amer. Math. Soc. **88** (1958), 327-330.

MathSciNet review:
0095414

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References | Similar Articles | Additional Information

**[1]**S. Banach,*Théorie des opérations linéaires*, Warsaw, 1932.**[2]**M. M. Day,*Notes on ordered linear spaces*, University of Illinois, 1950, unpublished.**[3]**-,*Means for the bounded functions and ergodicity of the bounded representations of semigroups*, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 89-108.**[4]**S. Kakutani,*Concrete representations of abstract*-*spaces*, Ann. of Math. vol. 42 (1941) pp. 523-537. MR**0004095 (2:318d)****[5]**M. G. Kreĭn and M. A. Rutman,*Linear operators leaving invariant a cone in a Banach space*[Uspehi Matematicheskii Nauk (N.S.) vol. 3 (23) (1948) pp. 3-95] Amer. Math. Soc. Translations, no. 26, 1950. MR**0038008 (12:341b)****[6]**A. Morse and R. Agnew,*Extensions of linear functionals, with applications to limits, integrals, measures, and densities*, Ann. of Math. vol. 39 (1938) pp. 20-30. MR**1503385****[7]**R. J. Silverman,*Invariant linear functions*, Trans. Amer. Math. Soc. vol. 81 (1956) pp. 411-424. MR**0082065 (18:492c)****[8]**-,*Means on semigroups and the Hahn-Banach extension property*, Trans. Amer. Math. Soc. vol. 83 (1956) pp. 222-237. MR**0084721 (18:910b)**

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DOI:
https://doi.org/10.1090/S0002-9947-1958-0095414-6

Article copyright:
© Copyright 1958
American Mathematical Society