Geodesic
Reducibility of function pairs in $H^\infty_\mathbb R$
Algebra i analiz, Tome 23 (2011) no. 6, pp. 131-143.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: corona theorem, Bézout equation, Blaschke product. 
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Raymond Mortini. Reducibility of function pairs in $H^\infty_\mathbb R$. Algebra i analiz, Tome 23 (2011) no. 6, pp. 131-143. http://geodesic.mathdoc.fr/item/AA_2011_23_6_a4/

[1] Corach G., Suárez F. D., “Stable rank in holomorphic function algebras”, Illinois J. Math., 29 (1985), 627–639 | MR | Zbl

[2] Corach G., Suárez F. D., “On the stable range of uniform algebras and $H^\infty$”, Proc. Amer. Math. Soc., 98 (1986), 607–610 | MR | Zbl

[3] Garnett J B., Bounded analytic functions, Pure Appl. Math., 96, Acad. Press, New York–London, 1981 | MR | Zbl

[4] Gorkin P., Mortini R., Nikolski N., “Norm controlled inversions and a corona theorem for $H^\infty$-quotient algebras”, J. Funct. Anal., 255 (2008), 854–876 | DOI | MR | Zbl

[5] Hoffman K., Banach spaces of analytic functions, Reprint of the 1962 original, Dover Publ. Inc., New York, 1988 | MR | Zbl

[6] Kulkarni S. H., Limaye B. V., Real function algebras, Monogr. Nextbooks Pure Appl. Math., 168, Marcel Dekker, New York, 1992 | MR | Zbl

[7] Mortini R., The covering dimension of a distinguished subset of the spectrum $M(H^\infty)$ of $H^\infty$ and the algebra of real symmetric and continuous functions on $M(H^\infty)$, Preprint

[8] Mortini R., Rupp R., “A note on some uniform algebra generated by smooth functions in the plane”, J. Funct. Spaces Appl. (to appear)

[9] Mortini R., Wick B., “The Bass and topological stable ranks of $H^\infty_\mathbb R(\mathbb D)$ and $A_\mathbb R(\mathbb D)$”, J. Reine Angew. Math., 636 (2009), 175–191 | DOI | MR | Zbl

[10] Mortini R., Wick B., “Spectral characteristics and stable ranks for the Sarason algebra $H^\infty+C$”, Michigan Math. J., 59 (2010), 395–409 | DOI | MR | Zbl

[11] Suárez F. D., “Čech cohomology and covering dimension for the $H^\infty$ maximal ideal space”, J. Funct. Anal., 123 (1994), 233–263 | DOI | MR | Zbl

[12] Treil S., “The stable rank of the algebra $H^\infty$ equals 1”, J. Funct. Anal., 109 (1992), 130–154 | DOI | MR | Zbl

[13] Wick B., “A note about stabilization in $A_\mathbb R(\mathbb D)$”, Math. Nachr., 282 (2009), 912–916 | DOI | MR | Zbl

[14] Wick B., “Stabilization in $H^\infty_\mathbb R(\mathbb D)$”, Publ. Mat., 54 (2010), 25–52 | MR | Zbl

[15] Wick B., “Corrigenda: `Stabilization in $H^\infty_\mathbb R(\mathbb D)$' ”, Publ. Mat., 55 (2011), 251–260 | MR | Zbl