Algebras Of Weakly Symmetric Functions On Spaces Of Lebesgue Measurable Functions

In this work, we investigate algebras of block-symmetric and weakly 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 ∈ [ 1 , + ∞ ) , and Lebesgue measurable essentially bounded functions on [ 0 , 1 ] . We construct generating systems of algebras of all weakly symmetric continuous complex-valued polynomials on these spaces. Also we establish conditions under which sets of weakly symmetric analytic functions are algebras.