We investigate a basisity problem in the space =lpA（D）and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the spacelpA（D）, 1≤p《∞, by W zn=λnzn＋1, n≥0, with re...We investigate a basisity problem in the space =lpA（D）and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the spacelpA（D）, 1≤p《∞, by W zn=λnzn＋1, n≥0, with respect to the standard basis λzn＋1 n≥0. Applying the so-called ＂discrete Duhamel product＂ technique, it is proven that for any integer k ≥1 the sequence {（wi＋nk）-1｜W ｜Ei）knf}n≥0 is a basic sequence in Ei ：=span{zi＋n ：n≥0} equivalent to the basis {zi＋n}n≥0 if and only if fb（i） 6= 0. We also investigate a Banach algebra structure for the subspaces Ei, i≥0.展开更多
基金supported by King Saud University,Deanship of Scientific Research,College of Science Research Center
文摘We investigate a basisity problem in the space =lpA（D）and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the spacelpA（D）, 1≤p《∞, by W zn=λnzn＋1, n≥0, with respect to the standard basis λzn＋1 n≥0. Applying the so-called ＂discrete Duhamel product＂ technique, it is proven that for any integer k ≥1 the sequence {（wi＋nk）-1｜W ｜Ei）knf}n≥0 is a basic sequence in Ei ：=span{zi＋n ：n≥0} equivalent to the basis {zi＋n}n≥0 if and only if fb（i） 6= 0. We also investigate a Banach algebra structure for the subspaces Ei, i≥0.
