Density of Balanced Convex-polynomials In LP(μ)

A bounded linear operator T on a locally convex space X is balanced convex-cyclic if there exists a vector x ۲ X such that the balanced convex hull of orb(T; x) is dense in X.A balanced convex-polynomial is a balanced convex combination of monomials f۱; z; z۲; z۳; : : : g.In this paper we prove that the balanced convex-polynomials are dense in Lp() when ([-۱; ۱]) = ۰.Our results are used to characterize which multiplication operators on various real Banach spaces are balanced convex-cyclic.Also,it is shown for certain multiplication operators that every nonempty closed invariant balanced convex-set is a closed invariant subspace.

کلیدواژه ها:

Balanced convex-polynomials ، Balanced convex-cyclic operators ، Hahn Banach theorem