On operator valued Haar unitaries and bipolar decompositions of R-diagonal elements
| Autor: | Dykema, Ken, Griffin, John |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the context of operator valued W*-free probability theory, we study Haar unitaries, R-diagonal elements and circular elements. Several classes of Haar unitaries are differentiated from each other. The term bipolar decomposition is used for the expression of an element as $vx$ where $x$ is self-adjoint and $v$ is a partial isometry, and we study such decompositions of operator valued R-diagonal and circular elements that are free, meaning that $v$ and $x$ are *-free from each other. In particular, we prove, when B=C^2, that if a $B$-valued circular element has a free bipolar decomposition with $v$ unitary, then it has one where $v$ normalizes $B$. Comment: The revision includes a few minor changes in the first four sections and a rewriting of Section 5. The rewriting highlights the results that are valid for general B by presenting them as lemmas, and then proceeding to consider the case of two-dimensional B for the remaining calculations. This paper will appear in the journal Integral Equations and Operator Theory |
| Databáze: | arXiv |
| Externí odkaz: |
|