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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show the existence of one point maximal antisymmetric sets for ${H^\infty } + C$ .

[1] S. Axler, Factorization of ${L^\infty }$ functions, Ann. of Math. (2) 106 (1977), 567-572. MR 0461142 (57:1127)
[2] E. Bishop, A generalization of the Stone Weierstrass theorem, Pacific J. Math. 11 (1961), 777-783. MR 0133676 (24:A3502)
[3] L. Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921-930. MR 0117349 (22:8129)
[4] -, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547-559. MR 0141789 (25:5186)
[5] K. F. Clancey and J. A. Gosselin, The local theory of Toeplitz operators, Illinois J. Math. 22 (1978), 449-458. MR 0482346 (58:2419)
[6] R. G. Douglas, Local Toeplitz operators, Proc. London Math. Soc. (3) 36 (1978), 243-272. MR 0482348 (58:2421)
[7] T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. MR 0410387 (53:14137)
[8] J. B. Garnett, Bounded analytic functions, Academic Press, New York, 1981. MR 628971 (83g:30037)
[9] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N.J., 1962. MR 0133008 (24:A2844)
[10] D. E. Marshall, Approximation and interpolation by inner functions, Thesis, Univ. of California, Los Angeles, Calif., 1976.
[11] W. Rudin, Real and complex analysis, 2nd ed, McGraw-Hill, New York, 1974. MR 0344043 (49:8783)
[12] D. Sarason, Algebras of functions on the unit circle, Bull. Amer. Math. Soc. 79 (1973), 286-299. MR 0324425 (48:2777)
[13] -, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405. MR 0377518 (51:13690)
[14] -, The Shilov and Bishop decompositions of ${H^\infty } + C$ , Conference on Harmonic Analysis in Honor of Antoni Zygmund, Volume II, Wadsworth, Belmont, California, 1983, pp. 461-474. MR 730085 (86a:46064)
[15] G. E. Shilov, On rings of functions with uniform convergence, Ukrain. Mat. Zh. 23 (1951), 404-411. MR 0054178 (14:884c)
[16] T. Wolff, Some theorems on vanishing mean oscillation, Thesis, Univ. of California, Berkeley, Calif., 1979.
[17] -, Two algebras of bounded functions. Duke Math. J. 49 (1982), 321-328. MR 659943 (84c:30051)