Matrix Transforms by Factorable Matrices
PDF

Keywords

Matrix transforms, factorable matrices, conservative and regular matrices, Riesz matrix.

How to Cite

Ants Aasma. (2018). Matrix Transforms by Factorable Matrices. Journal of Advances in Applied &Amp; Computational Mathematics, 5, 1–11. https://doi.org/10.15377/2409-5761.2018.05.1

Abstract

In the present paper an overview of existing results on matrix transforms of summability and absolute summability domains of matrix methods by factorable matrices is presented. Under the notion “multiplicative matrix” we consider a lower triangular matrix M = (mnk), where mnk = rnvk with rn,vk ϵ C.

https://doi.org/10.15377/2409-5761.2018.05.1
PDF

References

Aasma A, Dutta H and Natarajan PN. An Introductory Course in Summability Theory. JOHN WILEY & SONS: Hoboken 2017. https://doi.org/10.1002/9781119397786

Aasma A. Matrix Transforms of Summability Domains of Normal Series-to-Series Matrices. J Adv Appl Comput Math 2014; 1: 35-39. https://doi.org/10.15377/2409-5761.2014.01.02.1

Aasma A. Some inclusion theorems for absolute summability. Appl Math Lett 2012; 25(3): 404-407. https://doi.org/10.1016/j.aml.2011.09.023

Aasma A. Factorable matrix transforms of summability domains of Cesàro matrices. Int J Contemp Math Sci 2011; 6(44): 2201-2206.

Aasma A. On the matrix transformations of absolute summability fields of reversible matrices. Acta Math. Hungar 1994; 64(2): 143-150. https://doi.org/10.1007/BF01874118

Aasma A. Matrix transformations of summability fields of regular perfect matrix methods. Acta et Comment Univ Tartuensis 1994; 970: 3-12.

Aasma A. Transformations of summability fields. Acta et Comment Univ. Tartuensis 1987; 770: 38-51 (in Russian).

Akgun FA and Rhoades BE. Characterizations of H-J Matrices. Filomat 2016; 30 (3): 675-679. https://doi.org/10.2298/FIL1603675A

Akgun FA and Rhoades BE. Factorable generalized Hausdorff matrices. J Advanced Math Studies 2010; 3(1): 1-8.

Alpa'r L. On the linear transformations of series summable in the sense of Ces a' ro. Acta Math Hungar 1982; 39(1): 233-243. https://doi.org/10.1007/BF01895236

Alpa'r L. Sur certainschangements de variable des series de Faber. Studia Sci Math Hungar 1978; 13(1-2): 173-180.

Baron S. Introduction to the theory of summability of series. Valgus: Tallinn 1977 (in Russian).

Boos J. Classical and modern methods in summability. Oxford University Press: Oxford 2000.

Cooke RG. Infinite Matrices and Sequence Spaces. State Publishing Hous of Physics-Mathematics Literature: Moscow 1960 (in Russian).

Hardy GH. Divergent series. Oxford University Press: U.K. 1949.

Rhaly JrHC. Posinormality, coposinormality, and supraposinormality for some triangular operators. Sarajevo J Math 2016; 12(24)(1): 125-140.

Rhaly JrHC. Concerning the Cesàro matrix and its immediate offspring. Acta Math Univ Comenian (N.S.) 2015; 84(1): 27-38.

Rhaly Jr.HC. A superclass of the posinormal operators. New York J Math 2014; 20: 497-506.

Rhaly Jr.HC and Rhoades BE. The weighted mean operator on l2 with the weight sequence wn=n+1 is hyponormal. New Zealand J Math 2014; 44: 103-106.

Rhaly Jr.HC and Rhoades BE. Posinormal factorable matrices with a constant main diagonal. Rev Un Mat Argentina 2014; 55(1): 19-24.

Rhaly Jr.HC. A comment on coposinormal operators. Matematiche (Catania) 2013; 68 (1): 83-86.

Rhaly Jr.H.C and Rhoades BE. Conditions for factorable matrices to be hyponormal and dominant. Sib Elektron Mat Izv 2012; 9: 261-265.

Rhaly Jr.H.C. Posinormal factorable matrices whose interrupter is diagonal. Mathematica 2011; 53(76) (2): 181- 188.

Rhaly Jr.H.C. Discrete generalized Cesàro operators. Proc Amer Math So 1986; 34: 225-232.

Rhaly Jr.H.C. p- Cesàro matrices, Houston J Math 1989; 15(1): 137-146.

Rhaly Jr.H.C. Terraced matrices. Bull London Math Soc 1989; 21(4): 399-406. https://doi.org/10.1112/blms/21.4.399

Rhoades BE. An extension of two results of Hardy. Sarajevo J Math 2013; 9 (21): 95-100. https://doi.org/10.5644/SJM.09.1.08

Rhoades BE and Yildirim M. The spectra and fine spectra of factorable matrices on c0. Math Commun 2011; 16(1): 265- 270.

Rhoades BE and Sen P. Lower bounds for some factorable matrices. Int J Math Math Sci 2006: Art. ID 76135: 1-13.

Rhoades BE. Some sequence spaces which include c0 and c. Hokkaido Math J 2006; 35: 587-599. https://doi.org/10.14492/hokmj/1285766418

Rhoades BE and Yildirim M. Spectra for Factorable Matrices on lp . Integr equ oper Theory 2006; 55: 111-126.

Rhoades BE. Lower bounds for some matrices. Linear and Multilinear Algebra 1987; 20 (4): 47-352. https://doi.org/10.1080/03081088708817767

Rhoades BE. Lower bounds for some matrices II. Linear and Multilinear Algebra 1990; 26(1-2): 49-58. https://doi.org/10.1080/03081089008817965

Sinnamon G. Masked factorable matrices. Proc Royal Soc Edinburgh 2002; 132A: 245-254. https://doi.org/10.1017/S0308210500001608

Stieglitz M and Tietz H. Matrix transformationen von Folgenräumen: eine Ergebnis u!! bersicht. Math Z 1977; 154: 1-16. https://doi.org/10.1007/BF01215107

Thorpe B. Matrix transformations of Ces aro summable series. Acta Math Hungar 1986; 48(3-4): 255-265. https://doi.org/10.1007/BF01951350

Wilansky A. Functional Analysis. Blaisdell Publ Co: New York 1964.

Zeltser M. Factorable matrices and their associated Riesz matrices. Proc Estonian Acad Sci 2014; 6

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2018 Ants Aasma