Arcs defined by one-parameter semigroups of operators in Banach spaces with the Radon-Nikodym property

Byrne, Charles L.

doi:10.1090/S0002-9939-1975-0385635-2

Arcs defined by one-parameter semigroups of operators in Banach spaces with the Radon-Nikodym property
HTML articles powered by AMS MathViewer

by Charles L. Byrne PDF

Proc. Amer. Math. Soc. 53 (1975), 353-355 Request permission

Abstract:

It is shown that a recent theorem of Junghenn and Taam concerning the domain of the infinitesimal generator of a strongly continuous one-parameter semigroup of operators on a reflexive, locally convex topological vector space remains valid if the domain of the operators is a Banach space with the Radon-Nikodym property. A partial result is obtained for general Banach spaces.

References

Hugo D. Junghenn and C. T. Taam, Arcs defined by one-parameter semigroups of operators, Proc. Amer. Math. Soc. 44 (1974), 113–120. MR 331114, DOI 10.1090/S0002-9939-1974-0331114-7
M. A. Rieffel, The Radon-Nikodym theorem for the Bochner integral, Trans. Amer. Math. Soc. 131 (1968), 466–487. MR 222245, DOI 10.1090/S0002-9947-1968-0222245-2
S. Bochner and A. E. Taylor, Linear functionals on certain spaces of abstractly-valued functions, Ann. of Math. (2) 39 (1938), no. 4, 913–944. MR 1503445, DOI 10.2307/1968472
W. J. Davis and R. R. Phelps, The Radon-Nikodym property and dentable sets in Banach spaces, Proc. Amer. Math. Soc. 45 (1974), 119–122. MR 344852, DOI 10.1090/S0002-9939-1974-0344852-7
R. E. Huff, Dentability and the Radon-Nikodým property, Duke Math. J. 41 (1974), 111–114. MR 341033
R. R. Phelps, Dentability and extreme points in Banach spaces, J. Functional Analysis 17 (1974), 78–90. MR 0352941, DOI 10.1016/0022-1236(74)90005-6