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Range Inclusion for Multilinear Mappings: Applications

Published online by Cambridge University Press:  20 November 2018

C. K. Fong
C. K. Fong*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada
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Abstract

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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 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).

Keywords

47B4747B10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 3 , 01 September 1985 , pp. 317 - 320
Copyright
Copyright © Canadian Mathematical Society 1985

References

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