Symmetric polynomials on the complex Banach space of all Lebesgue integrable essentially bounded functions on the union of Lebesgue-Rohlin spaces

This work is devoted to the study of the algebra of all symmetric (invariant under composition of the variable with any measurable automorphism of the domain of the variable) continuous complex-valued polynomials on the complex Banach space of Lebesgue integrable essentially bounded complex-valued f...

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Bibliographic Details
Published in:AIP conference proceedings 2022-11, Vol.2483 (1)
Main Author: Vasylyshyn, Taras
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Banach spaces
Continuity (mathematics)
Mathematical analysis
Polynomials
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Summary:This work is devoted to the study of the algebra of all symmetric (invariant under composition of the variable with any measurable automorphism of the domain of the variable) continuous complex-valued polynomials on the complex Banach space of Lebesgue integrable essentially bounded complex-valued functions on the arbitrary union of Lebesgue-Rohlin measure spaces. We construct an algebraic basis of this algebra.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0115145