On the stable rank of Q_p∩H^∞

Abstract

Let 0 < p < 1. The stable rank of the Banach algebra Q _p ∩ H ^∞ is 1 if given f ₁, f ₂ in Q _p ∩ H ^∞ such that

there exists g in Q _p ∩ H ^∞ such that f ₁ + gf ₂ is invertible in Q _p ∩ H ^∞. As a partial answer to this problem, we prove the result when f ₁ is an inner function in Q _p .

Keywords:

• Q _p -spaces
• stable rank
• Carleson measures

AMS Subject Classifications:

• 30H05
• 32A37
• 46J15

Acknowledgements

Both authors share Grant 2005SGR00774. Also, J. Pau is partially supported by DGICYT Grant MTM2005-08984-C02-02, and D. Suárez is supported by the Ramón y Cajal program and DGICYT Grant MTM2005-00544.