ar X iv : 0 90 9 . 25 33 v 1 [ m at h . C V ] 1 4 Se p 20 09 TOPOLOGICAL STABLE RANK OF H ∞ ( Ω ) FOR CIRCULAR DOMAINS Ω
نویسندگان
چکیده
Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H(Ω) is equal to 2. The proof is based on Suarez’s theorem that the topological stable rank of H(D) is equal to 2, where D is the unit disk. We also show that for domains symmetric to the real axis, the Bass and topological stable ranks of the real symmetric algebra H R (Ω) are 2.
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