Symmetric polynomials on the Cartesian power of the real Banach space $L_\infty[0,1]$
Symmetric polynomials on the Cartesian power of the real Banach space $L_\infty[0,1]$
We construct an algebraic basis of the algebra of symmetric (invariant under composition of the variable with any measure preserving bijection of $[0,1]$) continuous polynomials on the $n$th Cartesian power of the real Banachspace $L_^{(\mathbb{R})}\infty[0,1]$ of Lebesgue measurable essentially bounded real valued functions on $[0,1].$ Also we describe the spectrum …