Skew exactness perturbation

Abstract

Abstract. We offer a perturbation theory for finite ascent and descent properties of bounded operators.

Skew exactness and range-kernel orthogonality

“…Thus ST = 0 iff T X ⊆ S −1 (0), and the pair (S, T ) is "exact" if the opposite inclusion holds. When they are either disjoint (intersection {0}), or add up to the whole space Y , we shall think of the pair (S, T ) as in some sense "skew exact" ( [12] §10.9; [13]; [14]). Among variations on this theme lies a certain "range-kernel orthogonality", based on James' Banach space orthogonality.…”

“…Weak orthogonality lies ( [14] (2.7)) between the conditions (1.4) and (1.6), and is transmitted by a hybrid of the conditions (1.3) and (1.5):…”