We prove that if A is a non-associative algebra over the field of real numbers, if there is a norm parallel to.parallel to on A satisfying parallel to xy parallel to = parallel to x parallel to parallel to y parallel to for all x, y in A, and if every one-generated subalgebra of A is finite-dimensional, then A is finite-dimensional. (C) 1997 Academic Press. [References: 34]
展开▼
