Decompositions of the maximal ideal space of 𝐿^{∞}

Gorkin, Pamela

doi:10.1090/S0002-9947-1984-0728701-1

Decompositions of the maximal ideal space of $L\sp{\infty }$

Author: Pamela Gorkin
Journal: Trans. Amer. Math. Soc. 282 (1984), 33-44
MSC: Primary 46J15; Secondary 30H05
DOI: https://doi.org/10.1090/S0002-9947-1984-0728701-1
MathSciNet review: 728701
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Abstract: In this paper we show the existence of one point maximal antisymmetric sets for ${H^\infty } + C$ .

[1] Sheldon Axler, Factorization of 𝐿^{∞} functions, Ann. of Math. (2) 106 (1977), no. 3, 567–572. MR 0461142, https://doi.org/10.2307/1971067
[2] Errett Bishop, A generalization of the Stone-Weierstrass theorem, Pacific J. Math. 11 (1961), 777–783. MR 0133676
[3] Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 0117349, https://doi.org/10.2307/2372840
[4] Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 0141789, https://doi.org/10.2307/1970375
[5] Kevin F. Clancey and John A. Gosselin, On the local theory of Toeplitz operators, Illinois J. Math. 22 (1978), no. 3, 449–458. MR 0482346
[6] R. G. Douglas, Local Toeplitz operators, Proc. London Math. Soc. (3) 36 (1978), no. 2, 243–272. MR 0482348, https://doi.org/10.1112/plms/s3-36.2.243
[7] Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR 0410387
[8] John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
[9] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. MR 0133008
[10] D. E. Marshall, Approximation and interpolation by inner functions, Thesis, Univ. of California, Los Angeles, Calif., 1976.
[11] Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974. McGraw-Hill Series in Higher Mathematics. MR 0344043
[12] Donald Sarason, Algebras of functions on the unit circle, Bull. Amer. Math. Soc. 79 (1973), 286–299. MR 0324425, https://doi.org/10.1090/S0002-9904-1973-13144-1
[13] Donald Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391–405. MR 0377518, https://doi.org/10.1090/S0002-9947-1975-0377518-3
[14] Donald Sarason, The Shilov and Bishop decompositions of 𝐻^{∞}+𝐶, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 461–474. MR 730085
[15] G. E. Šilov, On rings of functions with uniform convergence, Ukrain. Mat. Žurnal 3 (1951), 404–411 (Russian). MR 0054178
[16] T. Wolff, Some theorems on vanishing mean oscillation, Thesis, Univ. of California, Berkeley, Calif., 1979.
[17] Thomas H. Wolff, Two algebras of bounded functions, Duke Math. J. 49 (1982), no. 2, 321–328. MR 659943