References

  1. Alencar R., Aron R., Galindo P., Zagorodnyuk A. Algebras of symmetric holomorphic functions on \(\ell_p\). Bull. Lond. Math. Soc. 2003, 35 (2), 55–64. doi:10.1112/S0024609302001431
  2. Aron R., Galindo P., Pinasco D., Zalduendo I. Group-symmetric holomorphic functions on a Banach space. Bull. Lond. Math. Soc. 2016, 48 (5), 779–796. doi:10.1112/blms/bdw043
  3. Bandura A., Kravtsiv V., Vasylyshyn T. Algebraic basis of the algebra of all symmetric continuous polynomials on the Cartesian product of \(\ell_p\)-spaces. Axioms. 2022, 11 (2), art. no. 41. doi:10.3390/axioms11020041
  4. Chernega I., Galindo P., Zagorodnyuk A. Some algebras of symmetric analytic functions and their spectra. Proc. Edinb. Math. Soc. 2012, 55 (1), 125–142. doi:10.1017/S0013091509001655
  5. Chernega I., Holubchak O., Novosad Z., Zagorodnyuk A. Continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions on Banach spaces. Eur. J. Math. 2020, 6 (1), 153–163. doi:10.1007/s40879-019-00390-z
  6. Chopyuk Yu., Vasylyshyn T., Zagorodnyuk A. Rings of multisets and integer multinumbers. Mathematics 2022, 10 (5), art. no. 778. doi:10.3390/math10050778
  7. Galindo P., Vasylyshyn T., Zagorodnyuk A. The algebra of symmetric analytic functions on \(L_\infty\). Proc. Roy. Soc. Edinburgh Sect. A 2017, 147 (4), 743–761. doi:10.1017/S0308210516000287
  8. Galindo P., Vasylyshyn T., Zagorodnyuk A. Symmetric and finitely symmetric polynomials on the spaces \(\ell_\infty\) and \(L_\infty[0,+\infty)\). Math. Nachr. 2018, 291 (11–12), 1712–1726. doi:10.1002/mana.201700314
  9. Galindo P., Vasylyshyn T., Zagorodnyuk A. Analytic structure on the spectrum of the algebra of symmetric analytic functions on \(L_\infty\). Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 2020, 114, article number 56. doi:10.1007/s13398-020-00791-w
  10. González M., Gonzalo R., Jaramillo J.A. Symmetric polynomials on rearrangement invariant function spaces. J. Lond. Math. Soc. 1999, 59 (2), 681–697. doi:10.1112/S0024610799007164
  11. Halushchak S.I. Spectra of some algebras of entire functions of bounded type, generated by a sequence of polynomials. Carpatian Math. Publ. 2019, 11 (2), 311–320. doi:10.15330/cmp.11.2.311-320
  12. Halushchak S.I. Isomorphisms of some algebras of analytic functions of bounded type on Banach spaces. Mat. Stud. 2021, 56 (1), 107–112. doi:10.30970/MS.56.1.106-112
  13. Kravtsiv V., Vasylyshyn T., Zagorodnyuk A. On algebraic basis of the algebra of symmetric polynomials on \(\ell_p(\mathbb{C}^n)\). J. Funct. Spaces 2017, 2017, article ID 4947925. doi:10.1155/2017/4947925
  14. Nemirovskii A. S., Semenov S. M. On polynomial approximation of functions on Hilbert space. Mat. USSR Sbornik 1973, 21 (2), 255–277. doi:10.1070/SM1973v021n02ABEH002016
  15. Vasylyshyn T. Algebras of entire symmetric functions on spaces of Lebesgue measurable essentially bounded functions. J. Math. Sci. (N.Y.) 2020, 246 (2), 264–276. doi:10.1007/s10958-020-04736-x
  16. Vasylyshyn T. Symmetric polynomials on \((L_p)^n\). Eur. J. Math. 2020, 6 (1), 164–178. doi:10.1007/s40879-018-0268-3
  17. Vasylyshyn T.V. Symmetric polynomials on the Cartesian power of \(L_p\) on the semi-axis. Mat. Stud. 2018, 50 (1), 93–104. doi:10.15330/ms.50.1.93-104
  18. Vasylyshyn T.V. The algebra of symmetric polynomials on \((L_\infty)^n\). Mat. Stud. 2019, 52 (1), 71–85. doi:10.30970/ms.52.1.71-85
  19. Vasylyshyn T. Symmetric analytic functions on the Cartesian power of the complex Banach space of Lebesgue measurable essentially bounded functions on \([0,1]\). J. Math. Anal. Appl. 2022, 509 (2), 125977. doi:10.1016/j.jmaa.2021.125977
  20. Vasylyshyn T.V., Strutinskii M.M. Algebras of symmetric \(*\)-polynomials in the space \(\mathbb{C}^2\). J. Math. Sci. (N.Y.) 2021, 253 (1), 40–53. doi:10.1007/s10958-021-05211-x
  21. Vasylyshyn T.V., Zagorodnyuk A.V. Symmetric polynomials on the Cartesian power of the real Banach space \(L_\infty[0,1]\). Mat. Stud. 2020, 53 (2), 192–205. doi:10.30970/ms.53.2.192-205
  22. Vasylyshyn T., Zagorodnyuk A. Continuous symmetric 3-homogeneous polynomials on spaces of Lebesgue measurable essentially bounded functions. Methods Funct. Anal. Topology 2018, 24 (4), 381–398.
  23. Vasylyshyn T., Zhyhallo K. Entire symmetric functions on the space of essentially bounded integrable functions on the union of Lebesgue-Rohlin spaces. Axioms 2022, 11 (9), art. no. 460. doi:10.3390/axioms11090460