Symmetric Polynomials on Rearrangement-Invariant Function Spaces

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

“…In [8] Nemirovskii and Semenov described algebraic bases of algebras of continuous symmetric polynomials on real spaces ℓ , where 1 ≤ < +∞. Their results were generalized by González et al [7] to real separable rearrangement-invariant sequence spaces.…”

“…Algebras of polynomials and analytic functions on a Banach space which are invariant (symmetric) with respect to a group of linear operators ( ) acting on were studied by a number of authors [1][2][3][4][5][6][7][8][9][10] (see also a survey [11]). If has a symmetric structure, then it is natural to consider the case when ( ) is a group of operators which preserve this structure.…”

Estimates of Disjoint Sequences in Banach Lattices and R.I. Function Spaces

“…Now, according to [9] the space L p,q [0, 1] has a separating polynomial. This is not possible, since by [13] …”

Homomorphisms of the algebra of symmetric analytic functions on $\ell_1$

“…Symmetric polynomials on rearrangement-invariant function spaces were studied in [7,8]. In [7] it is proved that the polynomials…”