A form of infinite-dimensional polytopes
Following Kadec, an infinite-dimensional polytope, or K-polytope is defined as a closed convex bounded subset of a Banach space such that its intersection with any finite-dimensional manifold is a polytope. Theorem. Let X be a Banach space such that its closed unit ball \(B_ X\) is a K-polytope. Let \(T:X\to Y\) be a continuous linear injective mapping into a Banach space Y with \(T(B_ X)\) closed. Then T is an isomorphism. As a consequence it is shown that the algebraic interior of a K-polytope coincides with its topological interior. Related references are [\textit{V. P. Fonf}, Mat. Zametki 30, 627-634 (1981; Zbl 0484.46019)] and [\textit{J. Lindenstrauss}, Isr. J. Math. 4 (1966), 235-242 (1967; Zbl 0148.113)].
algebraic interior of a K-polytope coincides with its topological interior
scientific article; zbMATH DE number 3895657