Abstract
We construct the element of the Cartesian square of the complex Banach space L ∞ [ 0,1 ] of all Lebesgue measurable essentially bounded functions on [ 0,1 ] by the predefined values of elementary symmetric polynomials on this element. Results of this work can be applied to the investigation of an algebraic basis of the algebra of continuous symmetric polynomials on the Cartesian square of the complex Banach space L ∞ [ 0,1 ] .
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