BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS
ACTA MATHEMATICA SCIENTIA, cilt.34, sa.5, ss.1655-1660, 2014 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 5
- Basım Tarihi: 2014
- Doi Numarası: 10.1016/s0252-9602(14)60111-9
- Dergi Adı: ACTA MATHEMATICA SCIENTIA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1655-1660
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
We investigate a basisity problem in the space l(A)(p)(D) and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the space l(A)(p)(D), 1 <= p < infinity, nu Wz(n) = lambda(n)z(n+1), n >= 0, with respect to the standard basis {z(n)}(n >= 0). Applying the so-called "discrete Duhamel product" techique, it is proven that for any integer k >= 1 the sequence {(w(i+nk))(-1) (W vertical bar E-i)(kn) f}(n >= 0) is a basic sequence in E-i := span (z(i+n) : n >= 0} equivalent to the basis {z(i+n)}(n >= 0) if and only if <(f)over cap>(i) not equal 0. We also investigate a Banach algebra structure for the subspaces E-i, i >= 0.