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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

1 vote
1 answer
136 views

Is $\textbf{FHILB}$ locally regular?

Is the category, $\textbf{FHILB}$, of finite dimensional Hilbert spaces and linear maps locally regular, where `locally regular' is defined like this http://ncatlab.org/nlab/show/locally+regular+cat …
King Kong's user avatar
  • 631
2 votes
1 answer
257 views

Cardinality of the set of Boolean subalgebras of the lattice of projections on a Hilbert space

I have a simple question I've managed to get myself quite confused about. Given a Hilbert space H, what do we know about the cardinality of (a) the set $P(H)$ of projection operators onto $H$ (equi …
King Kong's user avatar
  • 631