A matricial identity involving the self-commutator of a commuting $n$-tuple
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- by Raúl E. Curto and Ren Yi Jian PDF
- Proc. Amer. Math. Soc. 121 (1994), 461-464 Request permission
Abstract:
For a commuting n-tuple $a = ({a_1}, \ldots ,{a_n})$ of elements of a unital ${C^ \ast }$-algebra $\mathcal {A}$, we establish a matricial identity linking the self-commutator of a to the ${2^{n - 1}} \times {2^{n - 1}}$ matrix $\hat a$ that detects the Taylor invertibility of a. As a consequence, we obtain a simple proof of a result of D. Xia (Oper. Theory: Adv. Appl. 48 (1990), 423-448), which states that for commuting t-hyponormal n-tuples, ${\sigma _T}(a) = {\sigma _r}(a)$.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 461-464
- MSC: Primary 47B47; Secondary 46L99, 47A13, 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1994-1182700-9
- MathSciNet review: 1182700