-convexity and duality for almost summing operators.
A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.
Let {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.