Range Inclusion for Multilinear Mappings: Applications
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AbstractThe 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 DBC0(H) ⊆ DAL(H) if and only if DBC1(H) ⊆ DAL(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).
2017 ◽
Vol 11
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pp. 1850004
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2005 ◽
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pp. 2175-2193
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2005 ◽
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pp. 33-54
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1995 ◽
Vol 07
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pp. 1105-1121
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2007 ◽
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pp. 1-15
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1987 ◽
Vol 29
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pp. 99-104
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Vol 26
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pp. 141-143
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