Geodesic
On Compact Perturbations of Operators
Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 247-250

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

Recently R. G. Douglas showed [4] that if V is a nonunitary isometry and U is a unitary operator (both acting on a complex, separable, infinite dimensional Hilbert space ), then V — K is unitarily equivalent to V ⊕ U (acting on ⊕ ) where K is a compact operator of arbitrarily small norm. In this note we shall prove a much more general theorem which seems to indicate "why" Douglas' theorem holds (and which yields Douglas' theorem as a corollary). 
Anderson, Joel. On Compact Perturbations of Operators. Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 247-250. doi: 10.4153/CJM-1974-024-3
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