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Results tagged with norms
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user 50614
4
votes
Accepted
Proving a certain $ C^{*} $-algebraic inequality
The following argument seems easier, but there might be a still more fundamental one.
Notice that $ \phi: A^{\sim} \to \mathbb{C} $ above is also a $ C^{*} $-algebraic homomorphism. As $ C^{*} $-alge …
- 1,396
8
votes
1
answer
352
views
Proving a certain $ C^{*} $-algebraic inequality
Let $ A $ be a non-unital $ C^{*} $-algebra. Is there an ‘elementary’ way to prove, for all $ (a,\lambda) \in A \times \mathbb{C} $, the inequality
$$
|\lambda| \leq \sup_{b \in A, ~ \| b \| \leq 1} \ …
- 1,396
5
votes
2
answers
215
views
On the coincidence (or non-coincidence) of two norms defined on the quotient of a given Hilb...
Let $ A $ be a $ C^{\ast} $-algebra, $ I $ a closed two-sided ideal of $ A $, and $ \mathcal{E} $ a Hilbert $ A $-module. Let
$$
\mathcal{E}_{I}
\stackrel{\text{df}}{=}
\{ x \in \mathcal{E} \mid \lang …
- 1,396