Algebras of symmetric and block-symmetric functions on spaces of Lebesgue measurable functions

In this work, we investigate algebras of symmetric and block-symmetric polynomials and analytic functions on complex Banach spaces of Lebesgue measurable functions for which the p th power of the absolute value is Lebesgue integrable, where p is an element of [ 1, + infinity ) , and Lebesgue measurable essentially bounded functions on [ 0, 1 ] . We show that spectra of Fre<acute accent>chet algebras of block-symmetric entire functions of bounded type on these spaces consist only of point-evaluation functionals. Also we construct algebraic bases of algebras of continuous block-symmetric polynomials on these spaces. We generalize the above-mentioned results to a wide class of algebras of symmetric entire functions.