Open AccessSOME PROPERTIES OF ELEMENTARY SYMMETRIC POLYNOMIALS ON THE CARTESIAN SQUARE OF THE COMPLEX BANACH SPACE L∞ [ 0,1 ]
Author(s) -
Taras Vasylyshyn
Publication year - 2018
Publication title -
prikarpatsʹkij vìsnik ntš. čislo
Language(s) - English
Resource type - Journals
ISSN - 2304-7399
DOI - 10.31471/2304-7399-2018-2(46)-9-16
Subject(s) - mathematics , square (algebra) , cartesian coordinate system , banach space , bounded function , pure mathematics , lp space , mathematical analysis , geometry
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 ] .