Abstract theory of abelian operator algebras: an application of forcing
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- by Thomas J. Jech
- Trans. Amer. Math. Soc. 289 (1985), 133-162
- DOI: https://doi.org/10.1090/S0002-9947-1985-0779056-9
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Abstract:
The abstract abelian operator theory is developed from a general standpoint, using the method of forcing and Boolean-valued models.References
- Paul Cohen, The independence of the continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1143–1148. MR 157890, DOI 10.1073/pnas.50.6.1143
- J. M. G. Fell and J. L. Kelley, An algebra of unbounded operators, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 592–598. MR 51439, DOI 10.1073/pnas.38.7.592
- Paul R. Halmos, Naive set theory, Undergraduate Texts in Mathematics, Springer-Verlag, New York-Heidelberg, 1974. Reprint of the 1960 edition. MR 0453532
- Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
- Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I, Pure and Applied Mathematics, vol. 100, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. Elementary theory. MR 719020
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- 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
- Frigyes Riesz and Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR 0071727
- Roman Sikorski, Boolean algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 25, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0126393
- Robert M. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1–56. MR 265151, DOI 10.2307/1970696
- Robert M. Solovay, Real-valued measurable cardinals, Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428. MR 0290961
- M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), no. 1, 37–111. MR 1501865, DOI 10.1090/S0002-9947-1936-1501865-8
- M. H. Stone, A general theory of spectra. I, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 280–283. MR 2023, DOI 10.1073/pnas.26.4.280
- Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728
- Gaisi Takeuti, Two applications of logic to mathematics, Kanô Memorial Lectures, Vol. 3, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1978. MR 0505474
- P. Vopěnka, The limits of sheaves over extremally disconnected compact Hausdorff spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 1–4 (English, with Russian summary). MR 225318
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 289 (1985), 133-162
- MSC: Primary 03E40; Secondary 03C60, 46Q05
- DOI: https://doi.org/10.1090/S0002-9947-1985-0779056-9
- MathSciNet review: 779056