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1 - A note on spectral mapping theoremJournal of Linear and Topological Algebra , Issue 5 , Year , Autumn 2018This paper aims to present the well-known spectral mapping theorem for multi-variable functions.This paper aims to present the well-known spectral mapping theorem for multi-variable functions. Manuscript profile -
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2 - On the h-Jensen's operator inequalityJournal of Linear and Topological Algebra , Issue 2 , Year , Spring 2022In this paper, we prove Jensen's operator inequality for an h-convex function and we point out the results for classes of continuous fields of operators. Also, some generalizations of Jensen's operator inequality and some pro MoreIn this paper, we prove Jensen's operator inequality for an h-convex function and we point out the results for classes of continuous fields of operators. Also, some generalizations of Jensen's operator inequality and some properties of the h-convex function are given. Manuscript profile -
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3 - New lower bound for numerical radius for off-diagonal $2\times 2$ matricesJournal of Linear and Topological Algebra , Issue 1 , Year , Winter 2024New norm and numerical radius inequalities for operators on Hilbert space are given. Among other inequalities, we prove that if $ A, B \in B(H) $, then \[\Vert A \Vert - \frac{3 \Vert A-B^* \Vert }{2} \leq \omega\left(\left[\begin{array}{cc} 0 & A \\ B & 0 \end{array}\r MoreNew norm and numerical radius inequalities for operators on Hilbert space are given. Among other inequalities, we prove that if $ A, B \in B(H) $, then \[\Vert A \Vert - \frac{3 \Vert A-B^* \Vert }{2} \leq \omega\left(\left[\begin{array}{cc} 0 & A \\ B & 0 \end{array}\right]\right).\] Moreover, $\omega(AB) \leq \frac{3}{2} \Vert Im(A) \Vert \Vert B \Vert + D_{B}\; \omega(A) $. In particular, if $ A $ is self-adjointable, then $\omega(AB) \leq D_{B} \Vert A \Vert$, where $D_{B}=\underset{\lambda \in \mathbb{C}}{\mathop{\inf}}\,\left\| B-\lambda I \right\|$. Manuscript profile