{"paper":{"title":"Interpolation of compact operators by the methods of Calder\\'on and Gustavsson-Peetre","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Cwikel, Nigel J. Kalton","submitted_at":"1992-10-08T15:45:24Z","abstract_excerpt":"Let $ X=(X_0,X_1)$ and $ Y=(Y_0,Y_1)$ be Banach couples and suppose $T: X\\to Y$ is a linear operator such that $T:X_0\\to Y_0$ is compact. We consider the question whether the operator $T:[X_0,X_1]_{\\theta}\\to [Y_0,Y_1]_{\\theta}$ is compact and show a positive answer under a variety of conditions. For example it suffices that $X_0$ be a UMD-space or that $X_0$ is reflexive and there is a Banach space so that $X_0=[W,X_1]_{\\alpha}$ for some $0<\\alpha<1.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9210206","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}