On block-supersymmetric polynomials on Banach spaces

Dmytro Faryma, Volodymyr Kimak, Viktoriia Kravtsiv, Andriy Zagorodnyuk

Abstract


We investigate algebras of block-supersymmetric polynomials on an infinite-dimensional Banach space \(\ell_p(\mathbb{C}^s)\) of absolutely \(p\)-convergent sequences of vectors in \(\mathbb{C}^s,\) and ring structures on the set \(\mathcal{M}_p\) of point evaluation homomorphisms of these algebras. In particular, we establish some necessary and sufficient conditions for a polynomial to be block-supersymmetric. Also, we describe complex ring homomorphisms of \(\mathcal{M}_p.\)

Keywords


symmetric polynomials on Banach spaces, supersymmetric polynomials, block-supersymmetric polynomials, symmetric analytic functions

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DOI: http://dx.doi.org/10.12958/adm2416

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