V. Les, V ) ? s f (W ) sont compacts dans B(H)

X. Si and . La, solution réduite (l'opérateur dans 5.1.4) alors X ? s f (V ) est un opérateur compact, i.e. l'

A. Im, B. Im, and B. Im, on a que Im A et s f (W ) sont des sous-espaces fermés qui sont les images de deux isométries partielles de même support initial Ainsi la condition 2) du théorème 5.2.3 est satisfaite, ce qui implique par le même théorème que (Im A) ? et (s f (W )) ? satisfont la même condition 2) Mais alors, Im A) ? ? s f (W ) ? (Im B) ?

S. Im, A. Im, B. Ker, X. , =. Im et al., Mais comme X est Fredholm d'index 0, donc Ker X = Ker X 0 =

. Preuve, B. *. On, and . Et-en-plus, comme A est semi-Fredholm à gauche et A ? B est compact, B est semi-Fredholm à gauche, donc Im B est fermée, donc la conclusion résulte de 4) dans le théorème précédent

. Preuve, Comme A est injectif et a l'image fermée, A est semi-Fredholm, donc B est lui aussi semi-Fredholm, en particulier l'image de B est fermée. D'autre part, comme A * est surjectif, Nous sommes donc dans les hypothèses du théorème 5.2.4, donc il existe X dans B(H) tel que X ? I est compact

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