On Algebraic Basis of the Algebra of Symmetric Polynomials on lp(Cn)

Abstract

We consider polynomials on spaces ℓ (C ), 1 ≤ < +∞, of -summing sequences of -dimensional complex vectors, which are symmetric with respect to permutations of elements of the sequences, and describe algebraic bases of algebras of continuous symmetric polynomials on ℓ (C ).

Representation of spectra of algebras of block-symmetric analytic functions of bounded type

“…Let us denote by P vs (X 2 ) the algebra of block-symmetric polynomials on X 2 . In [7] it was shown that the following vectors form an algebraic bases of "power" blocksymmetric polynomials of P vs (X 2 ) :…”

Supersymmetric Polynomials on the Space of Absolutely Convergent Series

“…Spectra of algebras H bs ( p ) were investigated also in [13,14]. Polynomials which are symmetric with respect to some other representations of the group of permutations of natural numbers were considered in [15][16][17].…”

The algebra of symmetric polynomials on $(L_\infty)^n$

“…In [2] it was shown that the trivial polynomial is the unique continuous symmetric polynomial on the complex Banach space of all Lebesgue measurable essentially bounded complex-valued functions on [0, +∞). Symmetric polynomials on Cartesian products of some Banach spaces were studied in [4,5,[8][9][10][11]. In particular, in [9] and [10] there were constructed algebraic bases of algebras of continuous symmetric polynomials on Cartesian powers of complex Banach spaces of Lebesgue measurable integrable in a power p, where 1 ≤ p < +∞, complex-valued functions on [0, 1] and [0, +∞) respectively.…”