Geodesic
Range Inclusion for Multilinear Mappings: Applications
Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 317-320

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DOI

The result of S. Grabiner [5] on range inclusion is applied for establishing the following two theorems: 1. For A, B ∊ L(H), two operators on the Hilbert space H, we have DB C0(H) ⊆ DAL(H) if and only if DB C1(H) ⊆ DA L(H), where DA is the inner derivation which sends S ∊ L(H) to AS - SA, C1(H) is the ideal of trace class operators and C0(H) is the ideal of finite rank operators. 2. (Due to Fialkow [3]) For A, B ∊ L(H), we write T(A, B) for the map on L(H) sending S to AS - SB. Then the range of T(A, B)is the whole L(H) if it includes all finite rank operators L(H).
DOI : 10.4153/CMB-1985-037-3
Mots-clés : 47B47, 47B10 
Fong, C. K. Range Inclusion for Multilinear Mappings: Applications. Canadian mathematical bulletin, Tome 28 (1985) no. 3, pp. 317-320. doi: 10.4153/CMB-1985-037-3
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     title = {Range {Inclusion} for {Multilinear} {Mappings:} {Applications}},
     journal = {Canadian mathematical bulletin},
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     year = {1985},
     volume = {28},
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     doi = {10.4153/CMB-1985-037-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-037-3/}
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