Stability of the inverses of interpolated operators with application to the Stokes system

Abstract We study the stability of isomorphisms between interpolation scales Banach spaces, including generated by well-known methods. develop a general framework for compatibility theorems, and our methods apply to cases. As by-product we prove that interpolated satisfy uniqueness-of-inverses. use obtained results lattice on function lattices demonstrate their application Calderón product spaces as well real method scales. also solvability Neumann problem Stokes system linear hydrostatics an arbitrary bounded Lipschitz domain with connected boundary in $$\mathbb {R}^n$$ R n , $$n\ge 3$$ ≥ 3 data some Lorentz $$L^{p,q}(\partial \Omega \mathbb {R}^n)$$ L p , q ( ∂ Ω ) over set $$\partial $$ equipped surface measure.