Algebraic Basis of the Algebra of All Symmetric Continuous Polynomials on the Cartesian Product of ℓp-Spaces
Andriy Bandura, Viktoriia Kravtsiv, Taras Vasylyshyn
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,+∞).
Topics & Concepts
MathematicsCartesian productBasis (linear algebra)Countable setPure mathematicsAlgebra over a fieldProduct (mathematics)Algebraic numberDiscrete mathematicsMathematical analysisGeometryAdvanced Banach Space TheoryApproximation Theory and Sequence SpacesHolomorphic and Operator Theory