2020/08/02 by Asekritova, Irina, Kruglyak, Natan, Mastyło, Mieczysław
#FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B70 #Secondary 47A13
paper · doi:10.48550/arxiv.2008.00449
We prove the stability of isomorphisms between Banach spaces generated by interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also the so-called ± or G1 and G2 methods defined by Peetre and Gustavsson-Peetre. This result is used to show the existence of solution of certain operator analytic equation. A by product of these results is a more general variant of the Albrecht-Müller result which states that the interpolated isomorphisms satisfy uniqueness-of-inverses between interpolation spaces. We show applications for positive operators between Calderón function lattices. We also derive connections between the spectrum of interpolated operators.