Relatively strongly \(p\)-sectorial linear operators (Q1594377)

Let \(F,G\) are Banach spaces, operator \(L\) is linear continuous operator from \(F\) to \(G\) and \(M\) is linear closed densely defined operator from \(F\) to \(G\). The authors introduce right and left \((L,p)\)-resolvents of operator \(M\): \[ R^L_{(\mu,p)}= \prod_{q=0}^p (\mu q L- M)^{- 1}L,\qquad L^L_{(\mu,p)}= \prod_{q=0}^p L(\mu q L- M)^{- 1}. \] In terms of these resolvents the relatively \((L,p)\)-sectorial operators are defined. In the paper the authors prove sufficient conditions for the operator \(M\) to be strongly \((L,p)\)-sectorial.