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arXiv · 2008.00449

A unified approach to compatibility theorems on invertible interpolated operators

Irina Asekritova·Natan Kruglyak·Mieczysław Mastyło
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Abstract

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 $\pm$ or $G_1$ and $G_2$ 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-M\"uller result which states that the interpolated isomorphisms satisfy uniqueness-of-inverses between interpolation spaces. We show applications for positive operators between Calder\'on function lattices. We also derive connections between the spectrum of interpolated operators.

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Irina Asekritova, Natan Kruglyak, Mieczysław Mastyło. 2020-08-02. A unified approach to compatibility theorems on invertible interpolated operators. https://arxiv.org/abs/2008.00449

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