Polynomial Projections inC[−1, 1] andL1(−1, 1) with Growthnγ, 0<γ⩽1/2 Original Research Article

Forγ∈(0, 1/2] we constructn-dimensional polynomial subspacesYnofC[−1, 1] andL1(−1, 1) such that the relative projection constantsλ(Yn, C[−1, 1]) andλ(Yn, L1(−1, 1)) grow asnγ. These subspaces are spanned by Chebyshev polynomials of the first and second kind, respectively. The spacesL1w(α, βwherewα, βis the weight function of the Jacobi polynomials and (α, β)∈{(−1/2, −1/2), (−1/2, 0), (0, −1/2)} are also studied.