A bounded linear operator T on a locally convex space X is balanced convex- cyclic if there exists a vector x ∈ 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 {1, z, z2, z3, . . . }. In this paper we prove that the balanced convex-polynomials are dense in Lp(μ) when μ([−1, 1]) = 0. 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.
Iloon Kashkooly,A. and Baseri,G. (2024). DENSITY OF BALANCED CONVEX-POLYNOMIALS IN Lp(μ). Mathematical Analysis and Convex Optimization, 4(1), 27-32. doi: 10.22034/maco.4.1.2
MLA
Iloon Kashkooly,A. , and Baseri,G. . "DENSITY OF BALANCED CONVEX-POLYNOMIALS IN Lp(μ)", Mathematical Analysis and Convex Optimization, 4, 1, 2024, 27-32. doi: 10.22034/maco.4.1.2
HARVARD
Iloon Kashkooly A., Baseri G. (2024). 'DENSITY OF BALANCED CONVEX-POLYNOMIALS IN Lp(μ)', Mathematical Analysis and Convex Optimization, 4(1), pp. 27-32. doi: 10.22034/maco.4.1.2
CHICAGO
A. Iloon Kashkooly and G. Baseri, "DENSITY OF BALANCED CONVEX-POLYNOMIALS IN Lp(μ)," Mathematical Analysis and Convex Optimization, 4 1 (2024): 27-32, doi: 10.22034/maco.4.1.2
VANCOUVER
Iloon Kashkooly A., Baseri G. DENSITY OF BALANCED CONVEX-POLYNOMIALS IN Lp(μ). MACO, 2024; 4(1): 27-32. doi: 10.22034/maco.4.1.2
Mathematical Analysis and Convex Optimization