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Issue 1 Vol 13 Winter 2024

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1 - A note on spectral mapping theorem
Z. Heydarbeygi B. Moosavi M. Shah Hosseini
20.1001.1.22520201.2018.07.04.3.2

This 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 - New lower bound for numerical radius for off-diagonal $2\times 2$ matrices
B. Moosavi M. Shah Hosseini
10.30495/jlta.2024.2002723.1602

New 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 More

New 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

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