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Results tagged with inequalities
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user 50614
for questions involving inequalities, upper and lower bounds.
1
vote
0
answers
117
views
Finding the infimum of the range of a certain non-negative function associated to a $ C^{*} ...
Let $ A $ be a non-trivial $ C^{*} $-algebra and $ n \in \mathbb{N} $. Setting $ \mathcal{D} \stackrel{\text{df}}{=} A^{n} \setminus \{ (0_{A},\ldots,0_{A}) \} $, we can define a function $ f: \mathca …
- 1,396
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