Spectra of algebras of block-symmetric analytic functions of bounded type

We investigate algebras of block-symmetric analytic functions on spaces $\ell_{p}(\mathbb{C}^s)$ which are $\ell_{p}$-sums $\mathbb{C}^{s}.$ consider properties algebraic bases polynomials,intertwining operations spectra the and representations as a semigroup exponential type several variables. All invertible elements described for case $p=1.$