Geodesic
Index Theory for Perturbations of Direct Sums of Normal Operators and Weighted Shifts
Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1152-1165

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we consider the construction of a norm-continuous index theory for unitary equivalence up to commutative normality of operators on a separable Jlilhert space, and establish some essentially best possible results in this direction for operators which can be written as direct sums of weighted shifts and normal operators. Indeed, for such operators we establish both a normcontinuous analogue and a norm-continuous extension of the elegant results of L. Brown, R. Douglas and P. Fillmore [4]. 
Berg, I. D. Index Theory for Perturbations of Direct Sums of Normal Operators and Weighted Shifts. Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1152-1165. doi: 10.4153/CJM-1978-096-4
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