c-numerical range of operator products on B(H)

2019/01/16 by Yanfang Zhang, Xiaochun Fang, Zhang, Yanfang +1
Mathematics · #47A12 #47B49 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A12 #msc:47B49

paper · pdf · doi:10.48550/arxiv.1901.05245

15 pages

arxiv created 2019/01/16 · arxiv updated 2019/01/17

Abstract

Let H be a complex Hilbert space of dimension no less than 2 and B(H) be the algebra of all bounded linear operators on H. We give the form of surjective maps on B(H) preserving c-numerical range of operator products when the maps satisfy preserving weak zero products. As a result, we obtain the characterization of surjective maps on Mn(C) preserving c-numerical range of operator products. The proof of the results depends on some propositions of operators in B(H), which are of different interest.

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