The convolution operation on the spectra of algebras of symmetric analytic functions

We 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.