Linear operators and conjugations on a Banach space - Motoyoshi Haruna (2019)
In this paper we study a conjugation on a Banach space X and show properties of operators concerning conjugation C and show spectral properties of such operators. Next we show spectral properties of an (m, C)-symmetry (isometry) operator T on a complex Banach space X . We prove that, for a C-doubly commuting pair (T, S), if T is an (m, C)-symmetry (isometry) and S is an (n, C)-symmetry (isometry), then T + S and T S are (m + n − 1, C)- symmetries (isometries).