Mathematical life

Geometry and Topology of Akilov's Beloved Spaces

V. V. Ivanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The answer is given to the question about the equivalence of the topologies generated by two complete norms in the same vector space. This question was raised in a personal letter from A. N. Kolmogorov to L. V. Kantorovich in 1935.

Keywords: Kantorovich's archive, Hamel basis, Bernstein theorem, Lebesque spaces, Banach norms, Kolmogorov's question.

UDC: 517.98

MSC: 46B04

Received January 20, 2011, published January 21, 2011