Greedy Expansions with Prescribed Coefficients in Hilbert Spaces

Abstract

Greedy expansions with prescribed coefficients, which have been studied by V. N. Temlyakov in Banach spaces, are considered here in a narrower case of Hilbert spaces. We show that in this case the positive result on the convergence does not require monotonicity of coefficient sequence C. Furthermore, we show that the condition sufficient for the convergence, namely, the inclusion C∈l2∖l1, can not be relaxed at least in the power scale. At the same time, in finite-dimensional spaces, the condition C∈l2 can be replaced by convergence of C to zero.