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- W2149346317 abstract "We show that if T=H+iK is the Cartesian decomposition of T∈B(H), then for α,β∈R, supα2+β2=1‖αH+βK‖=w(T). We then apply it to prove that if A,B,X∈B(H) and 0≤mI≤X, thenm‖Re(A)−Re(B)‖≤w(Re(A)X−XRe(B))≤12supθ∈R‖(AX−XB)+eiθ(XA−BX)‖≤‖AX−XB‖+‖XA−BX‖2, where Re(T) denotes the real part of an operator T. A refinement of the triangle inequality is also shown." @default.
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- W2149346317 date "2015-04-01" @default.
- W2149346317 modified "2023-09-29" @default.
- W2149346317 title "Cartesian decomposition and numerical radius inequalities" @default.
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- W2149346317 doi "https://doi.org/10.1016/j.laa.2014.12.016" @default.
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