The Weak Chebyshev X-Greedy Algorithm in the unweighted Bergman space

We study a greedy algorithm called the Weak Chebyshev X-Greedy Algorithm (WCXGA) and investigate its application to unweighted Bergman spaces. We first show that the WCXGA converges for a wide class of real and complex Banach spaces and dictionaries. We then prove that certain Bergman spaces and their holomorphic monomial dictionaries belong to the class of Banach spaces for which the WCXGA converges.