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Four characterizations of scalar-type operators with spectrum in a half-line. (English) Zbl 0871.47028

Summary: \(C^0\)-scalar-type spectrality criteria for operators \(A\) whose resolvent set contains the negative reals are provided. The criteria are given in terms of growth conditions on the resolvent of \(A\) and the semigroup generated by \(A\). These criteria 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.

MSC:

47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
47A60 Functional calculus for linear operators
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