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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

1. Davis, C. and Rosenthal, P., Solving linear operator equations, Canad. Math. J., 26 (1974), pp. 1384–1389.Google Scholar
2. Embry, M.R., Factorizations of operators on Banach space, Proc. Amer. Math. Soc, 38 (1973), pp. 587–590.Google Scholar
3. Fialkow, L., A note on normed ideals and the operator X - AX - XB, Israel J. Math., 32 (1973), pp. 331–348.Google Scholar
4. Fong, C.K., Range inclusion for normal derivations, Glasgow J. Math., 25 (1984), pp. 255—262 Google Scholar
5. Grabiner, S., Operator ranges and invariant subspaces, Indiana Univ. Math. J., 28 (1979), pp. 845–857.Google Scholar
6. Johnson, B.E. and Williams, J.P., The range of a normal derivation, Pacific J. Math. 58 (1975), pp. 105–122.Google Scholar
7. Schatten, R., Normed ideals of completely continuous operators, Springer, Berlin (1960).Google Scholar