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Operator matrices have played a significant role in the study of properties of the numerical radii of Hilbert space operators. This paper presents several new sharp upper bounds for the numerical radii of operator matrices in terms of certain complex combinations. The obtained results reveal many interesting properties of the numerical radius. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]