On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range

Denis Njue Kingangi

doi:doi:10.11648/j.pamj.20180701.12

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On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range

Denis Njue Kingangi

Published in Pure and Applied Mathematics Journal (Volume 7, Issue 1)

Received: 4 February 2018 Accepted: 8 March 2018 Published: 27 March 2018

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Abstract

Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of finite length and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range.

Published in	Pure and Applied Mathematics Journal (Volume 7, Issue 1)
DOI	10.11648/j.pamj.20180701.12
Page(s)	6-10
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Elementary Operator, Maximal Numerical Range, Rank-One Operator

References

[1]	D. N. King’ang’i, On the norm of elementary operator of length two, International Journal of Scientific and Innovative Mathematical Research 5 (2017), 34-38.
[2]	M. Baraa and M. Boumazgour, A lower bound of the norm of the operator ⟼axb+bxa, Extractamathematicae 16 (2001), 223-227.
[3]	M. Cabrera and A. Rodriguez, Non-degenerate ultraprimejordan-banach algebras: a zelmanorian treatment, Proc. london. math. soc 69 (1994), 576-604.
[4]	D. N. Kingangi, J. O. Agure and F. O. Nyamwala, On the norm of elementary operator, Advances in Pure Mathematics 4 (2014), 309-316.
[5]	M. Mathew, More properties of the product of two derivations of a c*-algebras, Bull. austral. math. soc 42 (1990), 115-120.
[6]	L. L. Stacho and B. Zalar, On the norm of jordan elementary operators in standard operator algebras, Publ. math. debreen 49 (1996), 127-134.
[7]	B. A. Odero, J. A. Ogonji, G. K. Rao, Norms of tensor product elementary operators, International Journal of Multidisciplinary sciences and Engineering 6 (2015), 29-32.
[8]	D. R. Jocic et al, Norm inequalities for elementary operators and other inner product type integral transformers with the spectra contained in the unit disc, Filomat 31 (2017), 197-206.
[9]	A. M. Wafula, N. B. Okelo, O. Ongati, Norms of normally represented elementary operators, International Journal of Modern Science and Technology 3 (2018), 10-26.
[10]	S. Paul and C. Gu, Tensor splitting properties of n-inverse pairs of operators, arXiv, 2015, 1-20.

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APA Style

Denis Njue Kingangi. (2018). On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range. Pure and Applied Mathematics Journal, 7(1), 6-10. https://doi.org/10.11648/j.pamj.20180701.12

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ACS Style

Denis Njue Kingangi. On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range. Pure Appl. Math. J. 2018, 7(1), 6-10. doi: 10.11648/j.pamj.20180701.12

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AMA Style

Denis Njue Kingangi. On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range. Pure Appl Math J. 2018;7(1):6-10. doi: 10.11648/j.pamj.20180701.12

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@article{10.11648/j.pamj.20180701.12,
  author = {Denis Njue Kingangi},
  title = {On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {1},
  pages = {6-10},
  doi = {10.11648/j.pamj.20180701.12},
  url = {https://doi.org/10.11648/j.pamj.20180701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180701.12},
  abstract = {Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of finite length and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range.},
 year = {2018}
}

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TY  - JOUR
T1  - On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range
AU  - Denis Njue Kingangi
Y1  - 2018/03/27
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180701.12
DO  - 10.11648/j.pamj.20180701.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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AB  - Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of finite length and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range.
VL  - 7
IS  - 1
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Author Information

Denis Njue Kingangi

Department of Mathematics & Computer Science, University of Eldoret, Eldoret, Kenya

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Plain Text BibTeX RIS

APA Style

Denis Njue Kingangi. (2018). On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range. Pure and Applied Mathematics Journal, 7(1), 6-10. https://doi.org/10.11648/j.pamj.20180701.12

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ACS Style

Denis Njue Kingangi. On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range. Pure Appl. Math. J. 2018, 7(1), 6-10. doi: 10.11648/j.pamj.20180701.12

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AMA Style

Denis Njue Kingangi. On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range. Pure Appl Math J. 2018;7(1):6-10. doi: 10.11648/j.pamj.20180701.12

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@article{10.11648/j.pamj.20180701.12,
  author = {Denis Njue Kingangi},
  title = {On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range},
  journal = {Pure and Applied Mathematics Journal},
  volume = {7},
  number = {1},
  pages = {6-10},
  doi = {10.11648/j.pamj.20180701.12},
  url = {https://doi.org/10.11648/j.pamj.20180701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20180701.12},
  abstract = {Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of finite length and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - On Norm of Elementary Operator: An Application of Stampfli’s Maximal Numerical Range
AU  - Denis Njue Kingangi
Y1  - 2018/03/27
PY  - 2018
N1  - https://doi.org/10.11648/j.pamj.20180701.12
DO  - 10.11648/j.pamj.20180701.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 6
EP  - 10
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20180701.12
AB  - Many researchers in operator theory have attempted to determine the relationship between the norm of an elementary operator of finite length and the norms of its coefficient operators. Various results have been obtained using varied approaches. In this paper, we attempt this problem by the use of the Stampfli’s maximal numerical range.
VL  - 7
IS  - 1
ER  -

Copy | Download