A Hilbert space whose Hamel dimension

A Hilbert space whose Hamel dimension A Hilbert space whose Hamel dimension and Hilbert dimension are different.

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The Hilbert space l² has the orthonormal basis (e_n) with e_n(m) = d_mn;m, n Î N. Hence its Hilbert dimension is À₀. But the set of all sequences x_a = < 1,a,a², a³, ¼ > , 0 < a < 1 is a linearly independent uncountable subset of l². Thus the Hamel dimension of l² isn't À₀.

Comment. This Hilbert dimension is probably the only one which this can happen.

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On 22 Feb 2001, 00:17.