Algebraic Basis of the Algebra of All Symmetric Continuous Polynomials on the Cartesian Product of <i>ℓ</i>_p-Spaces

Abstract

We construct a countable algebraic basis of the algebra of all symmetric continuous polynomials on the Cartesian product ℓp1×…×ℓpn, where p1,…,pn∈[1,+∞), and ℓp is the complex Banach space of all p-power summable sequences of complex numbers for p∈[1,+∞).

Keywords

• symmetric polynomial on a Banach space
• continuous polynomial on a Banach space
• algebraic basis
• space of <i>p</i>-summable sequences