Geodesic
Adjoint Abelian Operators on Banach Space
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 505-512

Voir la notice de l'article provenant de la source Cambridge University Press

I. In the first part of this paper we introduce a new class of operators, mentioned in the title. It is easy to say that these are a generalization of self-adjoint operators for Hilbert space. This is deceptive since it implies that the definition of self-adjointness is forced into the unnatural setting of a Banach space. We feel that the definition of adjoint abelian preserves the obvious distinction between a space and its dual. Certain attractive properties of self-adjoint operators have already been singled out and carried over to Banach space. Specifically, we mention the notion of hermitian (see 17; 11), and spectral type operators (see 4). There is some comparison of these concepts later. 
Stampfli, J. G. Adjoint Abelian Operators on Banach Space. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 505-512. doi: 10.4153/CJM-1969-058-4
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