Hahn-Banach type theorems for adjoint semigroups. (English) Zbl 0671.47035

It is shown that most of the Hahn-Banach theorems hold for the semigroup dual space \(X^{\odot}\) of a \(C_ 0\)-semigroup on a Banach space X. As an application we give a new proof of a recently discovered characterization of \(\odot\)-reflexivity.


47D03 Groups and semigroups of linear operators
46B10 Duality and reflexivity in normed linear and Banach spaces
Full Text: DOI EuDML


[1] Butzer, P.L., Berens, H.: Semigroups of operators and approximation. New York: Springer 1967 · Zbl 0164.43702
[2] Cl?ment, Ph., Diekmann, O., Gyllenberg, M., Heijmans, H.J.A.M., Thieme, H.R.: Perturbation theory for dual semigroups, Part I. The sun-reflexive case. Math. Ann.277, 709-725 (1987) · Zbl 0634.47039
[3] Dunford, N., Schwartz, J.: Linear operators, Part I. General theory. New York: Interscience 1958 · Zbl 0084.10402
[4] Pagter, B. de: A characterization of sun-reflexivity. Math. Ann.283, 511-518 (1989) · Zbl 0696.47039
[5] Phillips, R.S.: The adjoint semi-group. Pac. J. Math.5, 269-283 (1955) · Zbl 0064.11202
[6] Pazy, A.: Semigroups of linear operators and applications to partial differential equations Berlin Heidelberg New York: Springer 1983 · Zbl 0516.47023
[7] Rudin, W.: Functional analysis. New York: McGraw-Hill 1973 · Zbl 0253.46001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.