In the spectrum of the algebra of symmetric analytic functions of bounded type on p, 1 p < +∞, and along the same lines as the general non-symmetric case, we define and study a convolution operation and give a formula for the 'radius' function. It is also proved that the algebra of analytic functions of bounded type on 1 is isometrically isomorphic to an algebra of symmetric analytic functions on a polydisc of 1 . We also consider the existence of algebraic projections between algebras of symmetric polynomials and the corresponding subspace of subsymmetric polynomials.

a b s t r a c tWe show that the spectrum of the algebra of bounded symmetric analytic functions on ℓ p , 1 ≤ p < +∞ with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1, a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements.

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