Abstract
Let A be a positive (semidefinite) bounded linear operator on a complex Hilbert space \(\big ({\mathcal {H}}, \langle \cdot , \cdot \rangle \big )\). The semi-inner product induced by A is defined by \({\langle x, y\rangle }_A := \langle Ax, y\rangle \) for all \(x, y\in {\mathcal {H}}\) and defines a seminorm \({\Vert \cdot \Vert }_A\) on \({\mathcal {H}}\). This makes \({\mathcal {H}}\) into a semi-Hilbert space. For \(p\in [1,+\infty )\), the generalized A-joint numerical radius of a d-tuple of operators \({\mathbf {T}}=(T_1,\ldots ,T_d)\) is given by
Our aim in this paper is to establish several bounds involving \(\omega _{A,p}(\cdot )\). In particular, under suitable conditions on the operators tuple \({\mathbf {T}}\), we generalize the well-known inequalities due to Kittaneh (Studia Math 168(1):73–80, 2005).
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Conde, C., Feki, K. On some inequalities for the generalized joint numerical radius of semi-Hilbert space operators. Ricerche mat 73, 661–679 (2024). https://doi.org/10.1007/s11587-021-00629-6
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DOI: https://doi.org/10.1007/s11587-021-00629-6