Abstract
An earlier paper (Mh. Math.51, 278–297 (1949)) exploited the property ‖∣Tx‖∣2≤‖∣x‖∣ ‖∣T 2 x‖∣, and the same property for polynomials in the operatorT, as an aid in establishing spectral resolutions associated withT. The present paper uses the weaker property ‖∣T‖∣=‖∣T 2‖∣1/2=..., and its extension to polynomials, for the same purpose. Also considered are the possibility of equivalence between the two types of conditions, and the use of arithmethical hypotheses concerning the eigenvalues.
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Atkinson, F.V. The polynomial-normaloid property for Banach-space operators. Monatshefte für Mathematik 79, 273–283 (1975). https://doi.org/10.1007/BF01647328
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DOI: https://doi.org/10.1007/BF01647328