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.
Highlights
Introduction and preliminariesAs customary, we reserve for scalars and other capital letters denote general elements of the C -algebra B (H ) of all bounded linear operator acting on Hilbert space (H ; h ; i)
We present some new operator equalities and inequalities by using quadratic map in the framework of B (H )
We reserve for scalars and other capital letters denote general elements of the C -algebra B (H ) of all bounded linear operator acting on Hilbert space (H ; h ; i)
Summary
Shiva SHEYBANI1, Mohsen Erfanian OMIDVAR2, Mahnaz KHANEHGIR3, and Silvestru Sever DRAGOMIR4. 1;2;3Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, IRAN 4School of Computer Science and Mathematics Victoria University of Technology, PO Box 14428, MCMC 8001, Victoria, AUSTALIA
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
