STRUCTURE OF CONTINUOUS SYMMETRIC POLYNOMIALS ON THE SPACE OF ABSOLUTELY SUMMABLE SEQUENCES - Vasylyshyn, T. V.; Kotselovska, M.R. (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2025)
The work is devoted to the study of symmetric continuous homogeneous polynomials on the Banach space _1 over the field K{R, C} of all absolutely summable sequences of elements of K. We consider the notion of symmetry in the following sense. Every bijection τ on N generates some isometrical isomorphism J_τ: _1→_1 that rearranges elements of the standard Schauder basis according to τ. As a result, every subgroup S of the group of all bijections on N generates the group G_S of corresponding isometrical isomorphisms on _1. The structure of G_S-symmetric homogeneous continuous K-valued polynomials on _1 is investigated in the present work.