Abstract
The $$\mathcal {C}$$ -numerical radius of matrices has been defined and studied in many publications. Here, the $$\mathcal {C}$$ -numerical radius of matrices is generalized to the notion of $$\mathcal {C}$$ -numerical radius of bounded linear operator and some properties of it brought in light. Also, some upper bounds of this radius, specially for some operator matrices, studied. $$\mathcal {C}$$ -numerical radius of some special operator matrices is also derived.
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