Acta mathematica scientia, Series B >
BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS
Received date: 2012-06-25
Revised date: 2014-03-05
Online published: 2014-09-20
Supported by
This work was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.
We investigate a basisity problem in the space ?pA(D) and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the space ?pA(D) , 1 ≤ p < ∞, by Wzn = λnzn+1, n ≥0, with respect to the standard basis
{zn }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 f(i)≠0. We also investigate a Banach algebra structure for the subspaces Ei, i ≥0.
M. GüRDAL , M.T. GARAYEV , S. SALTAN . BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS[J]. Acta mathematica scientia, Series B, 2014 , 34(5) : 1655 -1660 . DOI: 10.1016/S0252-9602(14)60111-9
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