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.

参考文献

[1] Bozhinov N. Convolutional Representations of Commutants and Multipliers. Sofia Publ House Bulg Acad Sci, 1988

[2] Dimovski I. Convolutional Calculus. Sofia Publ House Bulg Acad Sci, 1982

[3] Fage M K, Nagnibida N I. The Equivalence Problem of Ordinary Linear Differential Operators (in Russian). Novosibirsk: Nauka, 1987

[4] G¨urdal M. On basisity problem in the spaces ?pA??D, 1 p < 1. Numerical Funct Anal Optimization, 2011, 32(1): 59–64

[5] G¨urdal M. Description of extended eigenvalues and extended eigenvectors of integration operator on the Wiener algebra. Expo Math, 2009, 27: 153–160

[6] Haslinger F. On some new bases in spaces of holomorphic functions//Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1 (Bucharest, 1981). Lecture Notes in Math, 1013. Berlin: Springer, 1983: 266–283

[7] Holub J. Shift basic sequences in the Wiener disk algebra. Proc Amer Math Soc, 1983, 88: 464–468

[8] Karaev M T. On some applications of the ordinary and extended Duhamel products. Siberian Math J, 2005, 46(3): 431–442

[9] Karaev M T. On extended eigenvalues and extended eigenvectors of some operator classes. Proc Amer Math Soc, 2006, 134: 2383–2392

[10] Karaev M T, G¨urdal M. Strongly splitting weighted shift operators on Banach spaces and unicellularity. Operators and Matrices, 2011, 5(1): 157–171

[11] Karaev M T, G¨urdal M, Saltan S. Some applications of Banach algebra techniques. Math Nachrichten, 2011, 284(13): 1678–1689

[12] Karaev M T, Saltan S. A Banach algebra structure forWiener algebra W??D of the disk. Complex Variables: Theory and Applications, 2005, 50(4): 299–305

[13] Merryfield K G, Watson S. A local algebra structure for Hp of the polydisk. Colloq Math, 1991: 73–79

[14] Saltan S, ¨Ozel Y. On some applications of A special integrodifferential operators. Journal of Function Spaces
and Applications, 2012, 2012: Article ID 894527

[15] Saltan S, Acar S. On the Solvability of Some System of Integro-Differential Equations. J Math Sci: Adv Appl, 2010, 5(1): 85–92

[16] Singer I. Bases in Banach Spaces, I. Berlin: Springer-Verlag, 1970

[17] Wigley N. The Duhamel product of analytic functions. Duke Math J, 1974, 41: 211–217

[18] Wigley N. A Banach algebra structure for Hp. Canad Math Bull, 1975, 18: 597–603

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

BASISITY PROBLEM AND WEIGHTED SHIFT OPERATORS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Dijana MOSIC. A NOTE ON THE REPRESENTATIONS FOR THE GENERALIZED DRAZIN INVERSE OF BLOCK MATRICES[J]. 数学物理学报(英文版), 2015, 35(6): 1483-1491.
[2]	Niraj KUMAR, Garima MANOCHA. A CLASS OF ENTIRE DIRICHLET SERIES AS AN FK-SPACE AND A FRECHET SPACE[J]. 数学物理学报(英文版), 2013, 33(6): 1571-1578.
[3]	张杰. THE CANONICAL BASIS FOR THE QUANTUM GROUP OF TYPE B₂[J]. 数学物理学报(英文版), 2013, 33(5): 1499-1506.
[4]	DEEPMALA, H.K. PATHAK. A STUDY ON SOME PROBLEMS ON EXISTENCE OF SOLUTIONS FOR NONLINEAR FUNCTIONAL-INTEGRAL EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(5): 1305-1313.
[5]	H. Azadi KENARY, A.R. ZOHDI, M. Eshaghi GORDJI. FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN -NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS[J]. 数学物理学报(英文版), 2013, 33(4): 1113-1118.
[6]	Muhammad IMRAN, Syed Ahtsham ul Haq BOKHARY, Ali AHMAD, Andrea SEMANICOVá-FE?OVCíKOVá. ON CLASSES OF REGULAR GRAPHS WITH CONSTANT METRIC DIMENSION[J]. 数学物理学报(英文版), 2013, 33(1): 187-206.
[7]	许天周, Rassias John Michael, 许婉欣. A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES[J]. 数学物理学报(英文版), 2012, 32(3): 866-892.
[8]	A. Ghaffari, S. Javadi, H. Khodaei. APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS[J]. 数学物理学报(英文版), 2012, 32(2): 783-792.
[9]	汤冬梅, 钟同德, 邱春晖. HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS[J]. 数学物理学报(英文版), 2012, 32(2): 586-604.
[10]	H.Seferoglu, N.Simsek. THE BANACH ALGEBRAS GENERATED BY OPERATORS WITH ONE-POINT SPECTRUM[J]. 数学物理学报(英文版), 2011, 31(2): 673-680.
[11]	Ali Ghaffari. A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS[J]. 数学物理学报(英文版), 2008, 28(3): 588-594.
[12]	余丹; 陈莘萌. ANOTHER TYPE OF GENERALIZED BALL CURVES AND SURFACES[J]. 数学物理学报(英文版), 2007, 27(4): 897-907.
[13]	Harun Polat; Feyzi Basar. SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m[J]. 数学物理学报(英文版), 2007, 27(2): 254-266.
[14]	杨长森. ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE[J]. 数学物理学报(英文版), 2003, 23(3): 351-.
[15]	丁立新, 康立山. CONVERGENCE RATES FOR A CLASS OF EVOLUTIONARY ALGORITHMS WITH ELITIST STRATEGY[J]. 数学物理学报(英文版), 2001, 21(4): 531-540.