The algebra of symmetric analytic functions on L ∞

Pablo Galindo; Taras Vasylyshyn; Andriy Zagorodnyuk

doi:10.1017/S0308210516000287

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We consider the algebra of holomorphic functions on L ∞ that are symmetric, i.e. that are invariant under composition of the variable with any measure-preserving bijection of [0, 1]. Its spectrum is identified with the collection of scalar sequences such that is bounded and turns to be separable. All this follows from our main result that the subalgebra of symmetric polynomials on L ∞ has a natural algebraic basis.

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Kravtsiv, Victoriia Vasylyshyn, Taras and Zagorodnyuk, Andriy 2017. On Algebraic Basis of the Algebra of Symmetric Polynomials on lp(Cn). Journal of Function Spaces, Vol. 2017, Issue. , p. 1.

Galindo, Pablo Vasylyshyn, Taras and Zagorodnyuk, Andriy 2018. Symmetric and finitely symmetric polynomials on the spaces and . Mathematische Nachrichten, Vol. 291, Issue. 11-12, p. 1712.

Jawad, Farah and Zagorodnyuk, Andriy 2019. Supersymmetric Polynomials on the Space of Absolutely Convergent Series. Symmetry, Vol. 11, Issue. 9, p. 1111.

Galindo, Pablo Vasylyshyn, Taras and Zagorodnyuk, Andriy 2020. Analytic structure on the spectrum of the algebra of symmetric analytic functions on $$L_\infty $$. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Vol. 114, Issue. 2,

Chernega, Iryna Holubchak, Oleh Novosad, Zoryana and Zagorodnyuk, Andriy 2020. Continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions on Banach spaces. European Journal of Mathematics, Vol. 6, Issue. 1, p. 153.

Vasylyshyn, T. V. 2020. Algebras of Entire Symmetric Functions on Spaces of Lebesgue-Measurable Essentially Bounded Functions. Journal of Mathematical Sciences, Vol. 246, Issue. 2, p. 264.

Vasylyshyn, T. and Zagorodnyuk, A. 2020. Symmetric polynomials on the Cartesian power of the real Banach space $L_\infty[0,1]$. Matematychni Studii, Vol. 53, Issue. 2, p. 192.

Zagorodnyuk, А. V. and Kravtsiv, V. V. 2020. Multiplicative Convolution on the Algebra of Block-Symmetric Analytic Functions. Journal of Mathematical Sciences, Vol. 246, Issue. 2, p. 245.

Vasylyshyn, Taras 2020. Symmetric polynomials on. European Journal of Mathematics, Vol. 6, Issue. 1, p. 164.

Halushchak, S.I. 2021. Isomorphisms of some algebras of analytic functions of bounded type on Banach spaces . Matematychni Studii, Vol. 56, Issue. 1, p. 106.

Vasylyshyn, Т. V. and Strutinskii, М. М. 2021. Algebras of Symmetric *-Polynomials in the Space ℂ2. Journal of Mathematical Sciences, Vol. 253, Issue. 1, p. 40.

Vasylyshyn, Taras 2022. Symmetric analytic functions on the Cartesian power of the complex Banach space of Lebesgue measurable essentially bounded functions on [0,1]. Journal of Mathematical Analysis and Applications, Vol. 509, Issue. 2, p. 125977.

Halushchak, Svitlana 2022. Algebras of analytic functions on Banach spaces, generated by countable sets of polynomials and their properties. Vol. 2644, Issue. , p. 030006.

Vasylyshyn, Taras and Zhyhallo, Kostiantyn 2022. Entire Symmetric Functions on the Space of Essentially Bounded Integrable Functions on the Union of Lebesgue-Rohlin Spaces. Axioms, Vol. 11, Issue. 9, p. 460.

Zagorodnyuk, A. and Kravtsiv, V. V. 2022. Spectra of algebras of block-symmetric analytic functions of bounded type. Matematychni Studii, Vol. 58, Issue. 1, p. 69.

Vasylyshyn, Taras 2022. Symmetric polynomials on the complex Banach space of all Lebesgue integrable essentially bounded functions on the union of Lebesgue-Rohlin spaces. Vol. 2644, Issue. , p. 030014.

Vasylyshyn, Taras 2022. Symmetric analytic functions on Cartesian powers of complex Banach spaces of complex-valued Lebesgue integrable in a power p ∈ [0, + ∞) functions on [0, 1] and [0, + ∞). Vol. 2644, Issue. , p. 030015.

Bandura, Andriy Kravtsiv, Viktoriia and Vasylyshyn, Taras 2022. Algebraic Basis of the Algebra of All Symmetric Continuous Polynomials on the Cartesian Product of ℓp-Spaces. Axioms, Vol. 11, Issue. 2, p. 41.

Novosad, Zoriana Vasylyshyn, Svitlana and Zagorodnyuk, Andriy 2023. Countably Generated Algebras of Analytic Functions on Banach Spaces. Axioms, Vol. 12, Issue. 8, p. 798.

Chernega, Iryna Galindo, Pablo and Zagorodnyuk, Andriy 2024. On the spectrum of the algebra of bounded‐type symmetric analytic functions on ℓ1$\ell _1$. Mathematische Nachrichten, Vol. 297, Issue. 10, p. 3835.

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