4 ms·
It is true that finite dimensional vector spaces are reflexive. But the broader claim that only finite dimensional vector spaces are reflexive is false. For exa
by RossBencina 6y ago
It is true that finite dimensional vector spaces are reflexive. But the broader claim that only finite dimensional vector spaces are reflexive is false. For example, Hilbert spaces are reflexive and infinite dimensional. See the last paragraph here:
https://en.wikipedia.org/wiki/Hilbert_space#Duality https://en.wikipedia.org/wiki/Hilbert_space#Duality
See also:
https://en.wikipedia.org/wiki/Reflexive_space https://en.wikipedia.org/wiki/Reflexive_space
- edflsafoiewq 6y agoOP is correct assuming "dual" is defined as all the linear functionals on a space. The dual of an infinite-dimensional space in this sense always has larger dimension than the original space. The difference comes in that for Hilbert spaces, "dual" is usually taken to mean only the continuous linear functionals.
- snicker7 6y agoeg "continuous" vs "algebraic" duals.