Vol. 89, No. 1, 1980

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On the lattice of all closed subspaces of a Hermitian space

Hans Keller

Vol. 89 (1980), No. 1, 105–110
Abstract

The purpose of the paper is to prove the following

Theorem: Let E be a vector space over a field K with char K2, and let ϕ be a nondegenerate hermitian form on E. Then the lattice of all orthogonally closed subspaces of (E,ϕ) is modular if and only if E is finite dimensional.

Mathematical Subject Classification 2000
Primary: 46C99
Secondary: 06C05, 15A63, 10C05
Milestones
Received: 10 May 1979
Published: 1 July 1980
Authors
Hans Keller