A MATRICIAL IDENTITY INVOLVING THE SELF-COMMUTATOR OF A COMMUTING N-TUPLE

Authors
CURTO RE JIAN R
Citation
Re. Curto et R. Jian, A MATRICIAL IDENTITY INVOLVING THE SELF-COMMUTATOR OF A COMMUTING N-TUPLE, Proceedings of the American Mathematical Society, 121(2), 1994, pp. 461-464
Citations number
6
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
121
Issue
2
Year of publication
1994
Pages
461 - 464
Database
ISI
SICI code
0002-9939(1994)121:2<461:AMIITS>2.0.ZU;2-W
Abstract
For a commuting n-tuple a = (a1, ..., a(n)) of elements of a unital C -algebra A, we establish a matricial identity linking the self-commuta tor of a to the 2n-1 x 2n-1 matrix a that detects the Taylor invertibi lity 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 tha t for commuting t-hyponormal n-tuples, sigma(T)(a) = sigma(r)(a).