Recent content by r-rashidi

Equivalence means:an unitary map exists between two spaces(isometric topological isomorphism )(unitary equivalence ) reza.

only two nonseprable Hilbert spaces can be INequivalent.two seprable Hilbert spaces certainly are equivalent.(this is the origin of Unrh efect and Hawking radiation) reza.

By Haag's theorem in QFT (Local Q.P by Haag)one can obtain two representations from one algebra that are not unitarity equivalent. but all seperable Hilbert spaces(with infinit daimension) are topologically isomorphe( for example: thorem 2.3.3,Mathematical Quantization,Nik Weaver,).it shows Fock...

thank you i think this example is true. but nonseparable Hilbert spaces have important role in physics for example Fock space in quantum filed theory(i think it is a nonseparable Hilbert spaces but i don't know prove of it).my aim of this question was to find a simple and straight example.

Does anybody know an example for a uncountable infinite dimensional Hilbert space?(with reference or prove).i know about Banach space:\L_{\infty} has uncountable dimension(Functional Analysis,Carl.L.Devito,Academic Press,Exercise(3.2),chapter I.).but it is not a Hilbert space. thank you.