Let $A$ be a bounded linear operator and $P$ a bounded linear projection on a Banach space $X$. We show that the operator semigroup $(e^{t(A-kP)})_{t \ge 0}$ converges to a semigroup on a subspace of $X$ as $k \to \infty$ and we compute the limit semigroup.
A note on absorption semigroups and regularity
The angle along a curve and range-kernel complementarity
Some remarks on orthogonality of bounded linear operators
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