Four characterizations of scalar-type operators with spectrum in a half-line
Volume 122 / 1997
Studia Mathematica 122 (1997), 39-54 DOI: 10.4064/sm-122-1-39-54
$C^0$-scalar-type spectrality criterions for operators A whose resolvent set contains the negative reals are provided. The criterions are given in terms of growth conditions on the resolvent of A and the semigroup generated by A. These criterions characterize scalar-type operators on the Banach space X if and only if X has no subspace isomorphic to the space of complex null-sequences.