{"paper":{"title":"Q.H.I. spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Valentin Ferenczi","submitted_at":"1996-01-26T00:00:00Z","abstract_excerpt":"A Banach space $X$ is said to be Q.H.I. if eve\\-ry infinite dimensional quo\\-tient spa\\-ce of $X$ is H.I.: that is, a space is Q.H.I. if the H.I. property is not only stable passing to subspaces, but also passing to quotients and to the dual. We show that Gowers-Maurey's space is Q.H.I.; then we provide an example of a reflexive H.I. space ${\\cal X}$ whose dual is not H.I., from which it follows that $\\cal X$ is not Q.H.I."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601204","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"}