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- W2028398220 abstract "Abstract Let A ∈ ℒ(C n ) and A 1 , A 2 be the unique Hermitian operators such that A = A 1 + i A 2 . The paper is concerned with the differential structure of the numerical range map n A : x ↦ (( A 1 x, x ), ( A 1 x, x )) and its connection with certain natural subsets of the numerical range W ( A ) of A . We completely characterize the various sets of critical and regular points of the map n A as well as their respective images within W ( A ). In particular, we show that the plane algebraic curves introduced by R. Kippenhahn appear naturally in this context. They basically coincide with the image of the critical points of n A ." @default.
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- W2028398220 date "1998-10-01" @default.
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- W2028398220 title "On the numerical range map" @default.
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- W2028398220 doi "https://doi.org/10.1017/s1446788700034996" @default.
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