# resolvent set

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## resolvent set

[ri′zäl·vənt ′set]
(mathematics)
Those scalars λ for which the operator T- λ I has a bounded inverse, where T is some linear operator on a Banach space, and I is the identity operator.
References in periodicals archive ?
The analytic model represents a subnormal operator as the multiplication by the independent variable of a space of vector-valued functions that are analytic on the resolvent set of its normal extension, says Xia.
1] := ([lambda]I-A)x[parallel], x [member of] D(A) (for some [lambda] fixed in the resolvent set [rho](A) of A), and [X.
alpha]] : Re([lambda]) > [omega]} [subset] [rho](A)) ([rho](A) being the resolvent set of A) and
We denote by [rho](A) the resolvent set of A and by [sigma](A) the spectrum of A.
where [rho](T) = C\[sigma](T) is the resolvent set of T.
iso](T) denotes the set of all isolated points of [sigma]'(T), and [rho](T) = C\[sigma]'(T) is the resolvent set of T [member of] A' with respect to A'.
The last theorem that we state in this section shows that the point spectrum, continuous spectrum, and resolvent set of a self-adjoint operator A and each of its associated left-definite operators [A.
11), the scheme Solve with the scaling D would indeed work for each fixed 7 in the resolvent set with optimal complexity.
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