On the operator-valued analogues of the semicircle, arcsine and Bernoulli laws (Q2857166)
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scientific article; zbMATH DE number 6221639
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the operator-valued analogues of the semicircle, arcsine and Bernoulli laws |
scientific article; zbMATH DE number 6221639 |
Statements
On the operator-valued analogues of the semicircle, arcsine and Bernoulli laws (English)
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31 October 2013
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operator-valued distributions
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free convolutions
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Boolean convolutions
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generalized Cauchy transform
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A non-commutative probability space is a pair \((\mathcal A,\varphi)\), where \(\mathcal A\) is a unital \(*\)-algebra over the complex numbers and \(\varphi:\mathcal A\to\mathbb C\) is a positive functional with \(\varphi(1)=1\). Let \(\mathcal B\) be a \(*\)-subalgebra of \(\mathcal A\). Then \((\mathcal A,E_\mathcal B)\) is called a \(\mathcal B\)-valued non-commutative \(C^*\)-probability space. In the paper, relations between operator-valued Bernoulli, arcsine and semicircular distributions are shown.
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