吉国兴,冯文英.导算子范数的一个估计[J].数学研究及应用,1989,9(3):382~384
导算子范数的一个估计
An estimate for the norm of a derivation
  
DOI:10.3770/j.issn:1000-341X.1989.03.014
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吉国兴 陕西师范大学 
冯文英 河北师范大学 
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      In this paper, a derivation δAB mapping into a ideal I of B(H) is considered, when A,B ∈B(H) and I is a norm ideal. If Ran(δAB)?I, let δAB:B(H)→I denote the induced operator and let λ be the scalar such that A- λ∈I, B-λ∈I, we estimate the norm of δAB as follows‖A-λ‖+‖B-λ‖≥‖δAB‖≥‖A- λ‖+‖B-λ‖ when WN(A-λ)∩WN(λ - B)≠?, where WN(A- λ) denotes the normalized maximal numerical range and ‖A-λ‖ denotes the norm of A-λ∈I. In particular when I=Cp(lp, we prove that ‖δABp=‖A-λ‖p+‖B-λ‖p if and only if ‖A-λ‖=‖A-λ‖p and WN(A-λ)∩WN(λ-B)≠?. At last, some examples show that the estimate as above is exact.
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