Let A be the generator of an analytic semigroup (eAt)t≥0 on a Banach space X, B be a bounded operator in X and K= AB- BA be the commutator. Assuming that there is a linear operator S having a bounded left-inverse operator Sl-1, such that ∫0∞‖SeAt‖‖eBt‖dt<∞, and the operator KSl-1 is bounded and has a sufficiently small norm, we show that ∫0∞‖e(A+B)t‖dt<∞, where (e(A+B)t)t≥0 is the semigroup generated by A+ B. In addition, estimates for the supremum- and L1-norms of the difference e( A + B ) t- eAteBt are derived.
|Journal||Results in Mathematics|
|State||Published - 1 Mar 2020|
- Banach space
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Applied Mathematics