On Cones Associated with Schauder Frames

Abstract

In this paper, we define cone C_F associated with Schauder frame F =({x_n}; {f_n}) in Banach spaces. A necessary and sucient condition for a cone C_F to be normal has been given. Also, we have obtained a sufficient condition for the cone C_F to be minihedral and show that the converse is not true in general. Moreover, we have given some necessary and sufficient conditions for the cone C_F to be generating and has a bounded base. Finally, a characterization of normalized Schauder frames of type P*, al₊ and w₀ and a sufficient condition for the cone C_F1 associated with normalized shrinking Schauder frame F₁ = {(e_nx_n; e_nf_n)} has been given.

Key words and phrases. Schauder frame, cones, minihedral.

1991 Mathematics Subject Classification. 42C15