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


  • T.V. Vasylyshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine


symmetric function, block-symmetric function, analytic function on Banach space, space of Lebesgue measurable functions, spectrum of algebra, algebraic basis
Published online: 2024-06-06


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 $p\in[1,+\infty),$ and Lebesgue measurable essentially bounded functions on $[0,1]$. We show that spectra of Fréchet 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.

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How to Cite
Vasylyshyn, T. Algebras of Symmetric and Block-Symmetric Functions on Spaces of Lebesgue Measurable Functions. Carpathian Math. Publ. 2024, 16, 174-189.

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