Numerical range and functional calculus in Hilbert space

147 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Intersections of several disks of the Riemann sphere as K-spectral sets (2008, background): “The setX is aspectralset for A if it is a K-spectral set withK = 1.”
Decay properties for functions of matrices over $C^*$-algebras (2013, unknown): “The field of values of a complex matrix appears in the context of bounds for functions of matrices thanks to a result by Crouzeix (see [21]):”
An Error Analysis of Galerkin Projection Methods for Linear Systems with Tensor Product Structure (2013, background): “08, and it has been conjectured that CCrouzeix = 2 [8].”
A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functions (2013, background): “The numerical range is a convenient set for bounding the norm ‖sn(A)‖: by a theorem of Crouzeix [12] we have ‖sn(A)‖ ≤ 11.08 max z∈W(A) |sn(z)|.”
H^\infty functional calculus and square function estimates for Ritt operators (2012, background): “See also [13], [11] for striking results in the case when F is equal to the numerical range of T .”