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The notion of the joint numerical range of several linear operators with respect to a sesquilinear form is introduced. Geometrical properties of the joint numerical range are studied, in particular, convexity and angle points, in connection with the algebraic properties of the operators. The main focus is on the finite dimensional case.doi:10.1017/s0004972700020724 fatcat:t75g35pj5ndd5dss4diuk34vju