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• W1979276832 abstract "The spectrum of a unilateral shift has circular symmetry. Here an operator is studied which has elliptical symmetry. Let U be the unweighted shift on a separable Hilbert space H, and let α be a nonzero complex number. The spectrum of the operator Uα = 12(αU+α−1U∗) is studied, and its resolvent is given in interesting form. The operator Uα is a generalization of the real part of the shift U: U1 = 12(U + U∗). If Dα denotes the diagonal operator with weights 1, α, α2,…, then formally Uα = UαU1Dα−1, but the spectrum of Uα equals the spectrum of U1 if and only if α=1." @default.
• W1979276832 created "2016-06-24" @default.
• W1979276832 creator A5082057470 @default.
• W1979276832 date "1992-05-01" @default.
• W1979276832 modified "2023-09-26" @default.
• W1979276832 title "A relative of the shift operator" @default.
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• W1979276832 doi "https://doi.org/10.1016/0024-3795(92)90165-7" @default.
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