Reducibility of function pairs in 𝐻^{∞}_{ℝ}

Mortini, Raymond

doi:10.1090/S1061-0022-2012-01227-6

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ISSN 1547-7371(online) ISSN 1061-0022(print)

Reducibility of function pairs in $H^\infty_{\mathbb{R}}$

Author: Raymond Mortini
Original publication: Algebra i Analiz, tom 23 (2011), nomer 6.
Journal: St. Petersburg Math. J. 23 (2012), 1013-1022
MSC (2010): Primary 30H05, 46H15, 30J10, 30H80
Posted: September 17, 2012
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Abstract: A short proof of a result by Brett Wick on the reducibility of function pairs in $H^{\infty }_ \mathbb{R}$ is presented, and some unusual properties of the solutions to the associated Bézout equations are unveiled.

1. Gustavo Corach and Fernando Daniel Suárez, Stable rank in holomorphic function algebras, Illinois J. Math. 29 (1985), no. 4, 627–639. MR 806470 (87b:46056)
2. Gustavo Corach and Fernando Daniel Suárez, On the stable range of uniform algebras and 𝐻^{∞}, Proc. Amer. Math. Soc. 98 (1986), no. 4, 607–610. MR 861760 (87m:46103), http://dx.doi.org/10.1090/S0002-9939-1986-0861760-1
3. John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1981. MR 628971 (83g:30037)
4. Pamela Gorkin, Raymond Mortini, and Nikolai Nikolski, Norm controlled inversions and a corona theorem for 𝐻^{∞}-quotient algebras, J. Funct. Anal. 255 (2008), no. 4, 854–876. MR 2433955 (2009h:30061), http://dx.doi.org/10.1016/j.jfa.2008.05.011
5. Kenneth Hoffman, Banach spaces of analytic functions, Dover Publications Inc., New York, 1988. Reprint of the 1962 original. MR 1102893 (92d:46066)
6. S. H. Kulkarni and B. V. Limaye, Real function algebras, Monographs and Textbooks in Pure and Applied Mathematics, vol. 168, Marcel Dekker Inc., New York, 1992. MR 1197884 (93m:46059)
7. Raymond Mortini, The covering dimension of a distinguished subset of the spectrum 𝑀(𝐻^{∞}) of 𝐻^{∞} and the algebra of real-symmetric and continuous functions on 𝑀(𝐻^{∞}), Topology Appl. 159 (2012), no. 3, 900–910. MR 2868890, http://dx.doi.org/10.1016/j.topol.2011.12.005
8. R. Mortini and R. Rupp, A note on some uniform algebra generated by smooth functions in the plane, J. Funct. Spaces Appl. Article ID 905650 (2012), 15 pages.
9. Raymond Mortini and Brett D. Wick, The Bass and topological stable ranks of 𝐻^{∞}_{ℝ}(𝔻) and 𝔸_{ℝ}(𝔻), J. Reine Angew. Math. 636 (2009), 175–191. MR 2572249 (2010m:46079), http://dx.doi.org/10.1515/CRELLE.2009.085
10. Raymond Mortini and Brett D. Wick, Spectral characteristics and stable ranks for the Sarason algebra 𝐻^{∞}+𝐶, Michigan Math. J. 59 (2010), no. 2, 395–409. MR 2677628 (2011j:46085), http://dx.doi.org/10.1307/mmj/1281531463
11. Fernando Daniel Suárez, Čech cohomology and covering dimension for the 𝐻^{∞} maximal ideal space, J. Funct. Anal. 123 (1994), no. 2, 233–263. MR 1283028 (95g:46100), http://dx.doi.org/10.1006/jfan.1994.1088
12. S. Treil, The stable rank of the algebra 𝐻^{∞} equals 1, J. Funct. Anal. 109 (1992), no. 1, 130–154. MR 1183608 (93h:46076), http://dx.doi.org/10.1016/0022-1236(92)90015-B
13. Brett D. Wick, A note about stabilization in 𝐴_{ℝ}(𝔻), Math. Nachr. 282 (2009), no. 6, 912–916. MR 2530887 (2010d:46065), http://dx.doi.org/10.1002/mana.200610779
14. Brett D. Wick, Stabilization in 𝐻_{ℝ}^{∞}(𝔻), Publ. Mat. 54 (2010), no. 1, 25–52. MR 2603587 (2011c:46112), http://dx.doi.org/10.5565/PUBLMAT_54110_02
15. Brett D. Wick, Corrigenda: “Stabilization in 𝐻^{∞}_{ℝ}(𝔻)” [MR2603587], Publ. Mat. 55 (2011), no. 1, 251–260. MR 2779583 (2012a:46090), http://dx.doi.org/10.5565/PUBLMAT_55111_11

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