Well-bounded operators of type (B) in a class of Banach spaces

Journal of the Australian Mathematical Society

Werner Ricker¹ 

关键词: 41 B 40;    47 D 05;   

DOI  :  10.1017/S1446788700028676

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

It is shown that in a Grothendieck space with the Dunford-Pettis property, the class of well-bounded operators of type (B) coincides with the class of scalar-type spectral operators with real spectrum. It turns out that in such Banach spaces, analogues of the classical theorems of Hille-Sz. Nagy and Stone concerned with the integral representation of C0-semigroups of normal operators and strongly continuous unitary groups in Hilbert spaces, respectively, are of a very special nature.

【 授权许可】

Unknown