Published by De Gruyter October 4, 2021

Poisson like matrix operator and its application in p-summable space

Taja Yaying , Bipan Hazarika , Merve İlkhan and M. Mursaleen

From the journal Mathematica Slovaca

https://doi.org/10.1515/ms-2021-0048

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Abstract

The incomplete gamma function Γ(a, u) is defined by

Γ ( a , u ) = ∫ u ∞ t a − 1 e − t d t ,

where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix P(μ)=(pnkμ) given by

p n k μ = n ! Γ ( n + 1 , μ ) e − μ μ k k ! ( 0 ≤ k ≤ n ) , 0 ( k > n ) ,

where μ > 0 is fixed. We introduce the sequence space ℓp(P(μ)) for 1 ≤ p ≤ ∞ and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space ℓp(P(μ)). We obtain Gurarii’s modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator P(μ) on sequence space c₀ has been investigated.

Keywords: Poisson matrix; incomplete gamma function; matrix transformations; compact operators; geometric properties; spectrum of matrix operator

MSC 2010: Primary: 46A45; Secondary: 26D15; 46B45; 46B20; 33B20

The research of the first author (T. Yaying) is supported by Science and Engineering Research Board (SERB), New Delhi, India under the grant number EEQ/2019/000082.

bh_gu@gauhati.ac.in

Acknowledgement

The authors would like to thank the referee for reading the manuscript carefully and making valuable suggestions that significantly improve the presentation of the paper. The first author (T. Yaying) is thankful to Dr. M. Q. Khan, Principal, Dera Natung Government College, Itanagar, for constant encouragement and administrative supports.

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Received: 2020-05-10

Accepted: 2020-11-02

Published Online: 2021-10-04

Published in Print: 2021-10-26

Poisson like matrix operator and its application in p-summable space

Abstract

Acknowledgement

References

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