ON THE NUMERICAL RANGE

@inproceedings{Shapiro2017ONTN,
  title={ON THE NUMERICAL RANGE},
  author={J. H. Shapiro},
  year={2017}
}
The inner product of a Hilbert space associates to each bounded linear operator thereon a continuous complex-valued quadratic form which—thanks to the polarization identity—uniquely determines the operator. The operator’s numerical range is the image under this quadratic form of the surface of the Hilbert-space unit ball; it is a set of complex numbers that contains its operator’s eigenvalues (if there are any), and whose closure contains the operator’s spectrum. A centuryold result of Toeplitz… Expand
113 Citations
ON THE MAXIMAL NUMERICAL RANGE OF ELEMENTARY OPERATORS
Numerical Range and Compressions of the Shift
The Numerical Range of Linear Operators on Hilbert Spaces
Partial Smoothness of the Numerical Radius at Matrices Whose Fields of Values are Disks
Product of operators and numerical range
Joint numerical ranges and compressions of powers of operators
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