On the Banach Algebra B(c(Nᵗ))

Authors

  • Orhan Tuğ Department of Mathematics Education, Faculty of Education, Tishk International University, Erbil, Iraq

DOI:

https://doi.org/10.23918/eajse.v4i4p84

Keywords:

Norlund Matrix, Sequence Spaces, Banach Algebras, Matrix Norm

Abstract

In this paper, we give some properties of the Banach Algebras of the bounded operators on the BK space c(Nt) which is the Nörlund domain in the convergent sequence space introduced by Tuğ and Bas¸ar (2016). We prove that the class (c(Nt),c(Nt)) is a Banach algebra with respect to the norm ∥A∥ =∥LA∥ for all A∈(c(Nt),c(Nt)).

References

Choudhary, B., & Nanda, S. (1989). Functional analysis with applications. Wiley.

Conway, J. B. (2013). A course in functional analysis (Vol. 96). Springer Science & Business Media.

De Malafosse, B. (2004). On the banach algebra (lp (a)). International Journal of Mathematics and Mathematical Sciences, 2004(60), 3187–3203.

de Malafosse, B. (2005). The banach algebra b (x), where x is a bk space and applications. Mat. Vesnik, 57(1-2), 41–60.

Hardy, G. H. (2000). Divergent series (Vol. 334). American Mathematical Soc.

Jarrah, A., & Malkowsky, E. (1990). Bk spaces, bases and linear operators. Ren. Circ. Mat. Palermo II, 52, 177–191.

Malkowsky, E. (2011). Banach algebras of matrix transformations between spaces of strongly bounded and summable sequences. Advances in Dynamical Systems and Applications, 6(1), 91–109.

Malkowsky, E., & Al, J. (2003). Ordinary, absolute and strong summmability and matrix transformations. MFA-03, to appear.

Malkowsky, E., & Djolovi´c, I. (2013). Banach algebras of matrix transformations between some sequence spaces related to l-strong convergence and boundedness. Applied Mathematics and Computation, 219(16), 8779–8789.

Mears, F. M. (1943). The inverse norlund mean. Annals of Mathematics, 401–410.

Tug, O., & Basar, F. (2016). On the domain of n¨orlund mean in the spaces of null and convergent sequences, twms j. Pure Appl. Math, 7(1), 76–87.

Wang, C.-S. (1978). On n¨orlund sequence spaces. Tamkang J. Math, 9(1), 269–274.

Downloads

Published

2019-06-01

Issue

Section

Articles

How to Cite

Tuğ, O. (2019). On the Banach Algebra B(c(Nᵗ)). EURASIAN JOURNAL OF SCIENCE AND ENGINEERING, 4(4), 84-90. https://doi.org/10.23918/eajse.v4i4p84

Similar Articles

1-10 of 40

You may also start an advanced similarity search for this article.