BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

doi:10.1016/S0252-9602(14)60111-9

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1655-1660.doi: 10.1016/S0252-9602(14)60111-9

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

M. GÜRDAL|M.T. GARAYEV|S. SALTAN

Suleyman Demirel University, Department of Mathematics, 32260 Isparta, Turkey； Department of Mathematics, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451, Saudi Arabia； Suleyman Demirel University, Department of Mathematics, 32260 Isparta, Turkey

收稿日期:2012-06-25 修回日期:2014-03-05 出版日期:2014-09-20 发布日期:2014-09-20
基金资助:
This work was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

M. GÜRDAL|M.T. GARAYEV|S. SALTAN

Suleyman Demirel University, Department of Mathematics, 32260 Isparta, Turkey； Department of Mathematics, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451, Saudi Arabia； Suleyman Demirel University, Department of Mathematics, 32260 Isparta, Turkey

Received:2012-06-25 Revised:2014-03-05 Online:2014-09-20 Published:2014-09-20
Supported by:
This work was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.

摘要/Abstract

摘要：

We investigate a basisity problem in the space ?^p_A(D) and in its invariant sub-spaces. Namely, let W denote a unilateral weighted shift operator acting in the space ?^p_A(D) , 1 ≤ p < ∞, by W_zⁿ = λ_nzⁿ⁺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 {(w_i+nk)⁻¹(W | E_i)^knf } _n≥0 is a basic sequence in E_i := span {z_i+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 E_i, i ≥0.

关键词: basis, basic sequence, discrete Duhamel product, Banach algebra, weighted shift operator

Abstract:

Key words: basis, basic sequence, discrete Duhamel product, Banach algebra, weighted shift operator

中图分类号:

46B15

M. GüRDAL, M.T. GARAYEV, S. SALTAN. BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS[J]. 数学物理学报(英文版), 2014, 34(5): 1655-1660.

M. GüRDAL, M.T. GARAYEV, S. SALTAN. BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS[J]. Acta mathematica scientia,Series B, 2014, 34(5): 1655-1660.

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BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

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