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- W2020876415 abstract "For a contraction A on a Hilbert space H, we define the index j(A) (resp., k(A)) as the smallest nonnegative integer j (resp., k) such that ker(I−Aj∗Aj) (resp., ker(I−Ak*Ak)∩ker(I−AkAk∗)) equals the subspace of H on which the unitary part of A acts. We show that if n=dimH<∞, then j(A)⩽n (resp., k(A)⩽⌈n/2⌉), and the equality holds if and only if A is of class Sn (resp., one of the three conditions is true: (1) A is of class Sn, (2) n is even and A is completely nonunitary with ‖An−2‖=1 and ‖An−1‖<1, and (3) n is even and A=U⊕A′, where U is unitary on a one-dimensional space and A′ is of class Sn−1)." @default.
- W2020876415 created "2016-06-24" @default.
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- W2020876415 date "2010-06-01" @default.
- W2020876415 modified "2023-10-14" @default.
- W2020876415 title "Unitary part of a contraction" @default.
- W2020876415 cites W1602120208 @default.
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- W2020876415 doi "https://doi.org/10.1016/j.jmaa.2010.01.040" @default.
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