The Bass stable rank for the real Banach algebra A(K)sym

We compute the Bass stable rank of the algebra A(K)sym of real-symmetric functions that are continuous on symmetric compact planar sets K and holomorphic in the interior K∘ of K. This answers a problem posed by Rupp and Sasane (2010) [24]. We also give a characterization of the reducible pairs in C(K), C(K)sym and A(K)sym.