# Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions

## Keywords:

symmetric function, weakly symmetric function, analytic function on an infinite dimensional space, space of Lebesgue measurable functions### Abstract

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 $p\in[1,+\infty),$ 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.

*Carpathian Math. Publ.*

**2023**,

*15*, 411-419.