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Results tagged with hilbert-spaces
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user 50614
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.
2
votes
1
answer
390
views
Strongly Continuous Group Actions on the $ C^{\ast} $-Algebra of Compact Operators on a Hilb...
Let $ \mathcal{H} $ be a not-necessarily-separable Hilbert space. Let $ G $ be a locally compact Hausdorff group. It is easy to see that if $ U: G \to \mathbb{U}(\mathcal{H}) $ is a norm-continuous ho …
- 1,396
4
votes
1
answer
380
views
A Hilbert-space completion of a Hilbert $ C^{*} $-module over a separable $ C^{*} $-algebra
Let $ B $ be a separable $ C^{*} $-algebra and $ \mathcal{E} $ a Hilbert $ B $-module. We know that $ B $ has a faithful state $ \phi $. Using $ \phi $, we can construct a $ \mathbb{C} $-valued pre-in …
- 1,396
2
votes
0
answers
73
views
A question on groupoids and measurable fields of Hilbert spaces
Suppose that we have the following data:
$ \mathcal{G} $ is a locally compact Hausdorff groupoid, with its source and
range maps denoted by $ s $ and $ r $ respectively.
$ (\lambda^{x})_{x \in \math …
- 1,396