Abstract
It is well-known that semi-groups T(t), t>O, of bounded self-adjoint operators under modest restrictions concerning measurability or boundedness are in fact continuous with respect to the uniform norm topology and can be completely described by means of the spectral measure of T(1). This note discusses analogous facts for generalized scalar operators on Banach spaces in the sense of Colojoara and Foias [1]. For groups of such operators a fairly complete and simple description can be given, while for semi-groups we have to impose some additional restrictions as examples show.
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Lutz, D. Gruppen und Halbgruppen verallgemeinerter Skalaroperatoren. Manuscripta Math 20, 105–117 (1977). https://doi.org/10.1007/BF01170719
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DOI: https://doi.org/10.1007/BF01170719