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Douglas algebras which admit codimension 1 linear isometries

Author(s): Keiji Izuchi
Journal: Proc. Amer. Math. Soc. 129 (2001), 2069-2074.
MSC (2000): Primary 46J15, 47B38
Posted: November 30, 2000
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Abstract:

Let $B$ be a Douglas algebra and let $B_b$ be its Bourgain algebra. It is proved that $B$ admits a codimension 1 linear isometry if and only if $B \not= B_b$. This answers the conjecture of Araujo and Font.

References:

[1]
J. Araujo and J. J. Font, Codimension 1 linear isometries on function algebras, Proc. Amer. Math. Soc. 127(1999), 2273-2281. MR 99j:46059

[2]
J. Araujo and J. J. Font, Linear isometries between subspaces of continuous functions, Trans. Amer. Math. Soc. 349(1997), 413-428. MR 97d:46026

[3]
S. Axler and P. Gorkin, Division in Douglas algebras, Michigan Math. J. 31(1984), 89-94. MR 85h:46075

[4]
S.-Y. Chang, A characterization of Douglas algebras, Acta Math. 137(1976), 81-89. MR 55:1074a

[5]
J. Cima and R. Timoney, The Dunford Pettis property for certain planner uniform algebras, Michigan Math. J. 34(1987), 99-104. MR 88e:46023

[6]
J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. MR 83g:30037

[7]
P. Gorkin, K. Izuchi, and R. Mortini, Bourgain algebras of Douglas algebras, Canad. J. Math. 44(1992), 797-804. MR 94c:46104

[8]
P. Gorkin, H. -M. Lingenberg, and R. Mortini, Homeomorphic disks in the spectrum of $H^\infty$, Indiana Univ. Math. J. 39(1990), 961-983. MR 92b:46082

[9]
C. Guillory, K. Izuchi and D. Sarason, Interpolating Blaschke products and division in Douglas algebras, Proc. Roy. Irish Acad. Sect. A84(1984), 1-7. MR 86j:46054

[10]
K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall, Englewood Cliffs, N.J., 1962. MR 24:A2844

[11]
K. Hoffman, Bounded analytic functions and Gleason parts, Michigan Math. J. 40(1993), 53-75.

[12]
K. Izuchi, Interpolating Blaschke products and factorization theorems, J. London Math. Soc. (2)50(1994), 547-567. MR 95k:46086

[13]
D. Marshall, Subalgebras of $L^\infty$ containing $H^\infty$, Acta Math. 137(1976), 91-98. MR 55:10746

[14]
D. Sarason, Algebras of functions on the unit circle, Bull. Amer. Math. Soc. 79(1973), 286-299. MR 48:2777

[15]
R. Younis, Division in Douglas algebras and some applications, Arch. Math. 45(1985), 555-560. MR 87b:46059

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Additional Information:

Keiji Izuchi
Affiliation: Department of Mathematics, Niigata University, Niigata 950-2181, Japan
Email: izuchi@math.sc.niigata-u.ac.jp

DOI: 10.1090/S0002-9939-00-05842-1
PII: S 0002-9939(00)05842-1
Received by editor(s): November 15, 1999
Posted: November 30, 2000
Additional Notes: Supported by Grant-in-Aid for Scientific Research (No.10440039), Ministry of Education, Science and Culture.
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2000, American Mathematical Society

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