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    Revista Colombiana de Matemáticas
    Volumen 28 [ 2] ( 1994) Páginas 83-91

    On two properties of the numerical range of a bounded Hilbert space operator

    Jaime Rodriguez Montes
    Universidad Nacional de Colombia, Bogotá

    Abstract. Necessary and sufficient conditions are given for the numerical range of a bounded space operator to have an empty interior. A sufficient condition for this set to be open is also established.

    Palabras claves. Hilbert and pre-Hilbert spaces; bounded, self-adjoint and normal operators; interior of a set; numerical range and spectrum of an operator; functions of class C^1

    Codigo AMS. 1991 Primary 47A12, Secondary 47B15.