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Results tagged with hilbert-spaces
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user 43915
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.
0
votes
1
answer
557
views
Schur's lemma for antiunitary operators on complex Hilbert spaces
Suppose to have a linear irreducible unitary representation $\rho:G\rightarrow U(H)$ on a complex Hilbert space $H$ with $G$ a generic group. Let $A$ be an $\textit{anti}$-linear operator such that
$ …
- 275
5
votes
1
answer
485
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When does an irreducible unitary real representation remain irreducible after complexifying it?
Consider a unitary real representation of a Lie group $G$ over a real Hilbert space $\mathcal{H}_\mathbb{R}$
\begin{equation}
\rho:G\rightarrow U(\mathcal{H}_{\mathbb{R}})
\end{equation}
Taking the c …
- 275
1
vote
1
answer
126
views
Integral representation of joint projection valued measures
Given two positive $\sigma$-finite measures $\mu_{1/2}$ on the spaces $X_{1/2}$ one can define the product measure $\mu_1\otimes\mu_2$ on the product space $X_1\times X_2$. It can be proved that the f …
- 275