Some results around quadratic maps

Mohsen Erfanian Omidvar; Shiva Sheybani; Mahnaz Khanehgır; Sever Dragomır

doi:10.31801/cfsuasmas.659689

Research Article

Year 2020, Volume: 69 Issue: 2, 1111 - 1118, 31.12.2020

Mohsen Erfanian Omidvar Shiva Sheybani Mahnaz Khanehgır Sever Dragomır

https://doi.org/10.31801/cfsuasmas.659689

Abstract

References

Amir, D., Characterizations of inner product spaces, Birkhauser Verlag, 1986.
Bauschke, H.H., Combettes, P.L., Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
Bhatia, R., Sharma, R., Some inequalities for positive linear maps, Linear Algebra Appl., 436(6) (2012), 1562--1571.
Cheung, W.S., Pečarić, J., Bohr's inequalities for Hilbert space operators, J. Math. Anal. Appl., 323(1) (2006), 403--412.
Choi, M.D., Hadwin, D., Nordgren, E., Radjavi, H., Rosenthal, P., On positive linear maps preserving invertibility, J. Funct. Anal. 59(3) (1984), 462--469.
Cvetkovski, Z., Inequalities: Theorems, Techniques and Selected Problems, Springer Science & Business Media, 2012.
Evans, D.E., Positive linear maps on operator algebras, Comm. Math. Phys., 48(1) (1976), 15--22.
Fu, X., Some generalizations of operator inequalities, J. Math. Inequal., 9(1) (2015), 101--105.
Fujii, M., Zuo, H., Matrix order in Bohr inequality for operators, Banach J. Math. Anal., 1 (2010), 21--27.
Furuta, T., Mićić Hot, J., Pečarić, J., Seo, Y., Mond-Pečarić method in operator inequalities, Monographs in Inequalities, Zagreb, 2005.
Gumus I.H., A note on a conjecture about Wielandt's inequality, Linear Multilinear Algebra, 63(9) (2015), 1909--1913.
Hirzallah, O., Non-commutative operator Bohr inequality, J. Math. Anal. Appl., 282(2) (2003), 578--583.
Lin, M., On an operator Kantorovich inequality for positive linear maps, J. Math. Anal. Appl., 402(1) (2013), 127--132.
Størmer, E., Positive linear maps of operator algebras, Acta Math., 110(1) (1963), 233--278.
Zhang, P., More operator inequalities for positive linear maps, Banach J. Math. Anal., 9(1) (2015), 166--172.

Some results around quadratic maps

Year 2020, Volume: 69 Issue: 2, 1111 - 1118, 31.12.2020

Mohsen Erfanian Omidvar Shiva Sheybani Mahnaz Khanehgır Sever Dragomır

https://doi.org/10.31801/cfsuasmas.659689

Abstract

This paper dedicated to study quadratic maps. We present some new operator equalities and inequalities by using quadratic map in the framework of B(H). Applications for particular case of interest are also provided. The parallelogram law is recovered and some other interesting operator equalities are established. Afterward, we get an extension of some well known inequalities such as, triangle inequality. Especially, Bohr's inequality is generalized to the context of quadratic map. Some results concerning this inequality are surveyed. We give an application of our results in the previous sections. We show that our results are a generalization of some well known works due to Fujii and Hirzallah.

Keywords

"Quadratic map, operator inequalities, absolute value

References

Amir, D., Characterizations of inner product spaces, Birkhauser Verlag, 1986.
Bauschke, H.H., Combettes, P.L., Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
Bhatia, R., Sharma, R., Some inequalities for positive linear maps, Linear Algebra Appl., 436(6) (2012), 1562--1571.
Cheung, W.S., Pečarić, J., Bohr's inequalities for Hilbert space operators, J. Math. Anal. Appl., 323(1) (2006), 403--412.
Choi, M.D., Hadwin, D., Nordgren, E., Radjavi, H., Rosenthal, P., On positive linear maps preserving invertibility, J. Funct. Anal. 59(3) (1984), 462--469.
Cvetkovski, Z., Inequalities: Theorems, Techniques and Selected Problems, Springer Science & Business Media, 2012.
Evans, D.E., Positive linear maps on operator algebras, Comm. Math. Phys., 48(1) (1976), 15--22.
Fu, X., Some generalizations of operator inequalities, J. Math. Inequal., 9(1) (2015), 101--105.
Fujii, M., Zuo, H., Matrix order in Bohr inequality for operators, Banach J. Math. Anal., 1 (2010), 21--27.
Furuta, T., Mićić Hot, J., Pečarić, J., Seo, Y., Mond-Pečarić method in operator inequalities, Monographs in Inequalities, Zagreb, 2005.
Gumus I.H., A note on a conjecture about Wielandt's inequality, Linear Multilinear Algebra, 63(9) (2015), 1909--1913.
Hirzallah, O., Non-commutative operator Bohr inequality, J. Math. Anal. Appl., 282(2) (2003), 578--583.
Lin, M., On an operator Kantorovich inequality for positive linear maps, J. Math. Anal. Appl., 402(1) (2013), 127--132.
Størmer, E., Positive linear maps of operator algebras, Acta Math., 110(1) (1963), 233--278.
Zhang, P., More operator inequalities for positive linear maps, Banach J. Math. Anal., 9(1) (2015), 166--172.

There are 15 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Mohsen Erfanian Omidvar 0000-0002-5395-8170 Shiva Sheybani This is me 0000-0002-7285-1571 Mahnaz Khanehgır This is me 0000-0002-7435-7307 Sever Dragomır 0000-0003-2902-6805
Publication Date	December 31, 2020
Submission Date	December 15, 2019
Acceptance Date	May 2, 2020
Published in Issue	Year 2020 Volume: 69 Issue: 2

Cite

APA	Erfanian Omidvar, M., Sheybani, S., Khanehgır, M., Dragomır, S. (2020). Some results around quadratic maps. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1111-1118. https://doi.org/10.31801/cfsuasmas.659689
AMA	Erfanian Omidvar M, Sheybani S, Khanehgır M, Dragomır S. Some results around quadratic maps. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1111-1118. doi:10.31801/cfsuasmas.659689
Chicago	Erfanian Omidvar, Mohsen, Shiva Sheybani, Mahnaz Khanehgır, and Sever Dragomır. “Some Results Around Quadratic Maps”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1111-18. https://doi.org/10.31801/cfsuasmas.659689.
EndNote	Erfanian Omidvar M, Sheybani S, Khanehgır M, Dragomır S (December 1, 2020) Some results around quadratic maps. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1111–1118.
IEEE	M. Erfanian Omidvar, S. Sheybani, M. Khanehgır, and S. Dragomır, “Some results around quadratic maps”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1111–1118, 2020, doi: 10.31801/cfsuasmas.659689.
ISNAD	Erfanian Omidvar, Mohsen et al. “Some Results Around Quadratic Maps”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1111-1118. https://doi.org/10.31801/cfsuasmas.659689.
JAMA	Erfanian Omidvar M, Sheybani S, Khanehgır M, Dragomır S. Some results around quadratic maps. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1111–1118.
MLA	Erfanian Omidvar, Mohsen et al. “Some Results Around Quadratic Maps”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1111-8, doi:10.31801/cfsuasmas.659689.
Vancouver	Erfanian Omidvar M, Sheybani S, Khanehgır M, Dragomır S. Some results around quadratic maps. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1111-8.