Geodesic
On a Family of Generalized Numerical Ranges
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 678-685

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this note, an operator will always mean a bounded linear operator acting on a Hilbert space X into itself, unless otherwise stated. The class Cρ (0 < ρ < ∞ ) of operators, considered by Sz.-Nagy and Foiaş [5], is defined as follows: An operator T is in Cρ if Tnx = p PUnx for all x ∊ X, n = 1, 2, . . . , where U is a unitary operator on some Hilbert space Y containing X as a subspace, and P is the orthogonal projection of Y onto X. In [2] Holbrook defined the operator radii wρ (·) (0 < ρ ≦ ∞ ) as the generalized Minkowski distance functionals on the Banach algebra of bounded linear operators on X, i.e., and w∞(T) = r(T), the spectral radius of T [2, Theorem 5.1]. 
Lin, C.-S. On a Family of Generalized Numerical Ranges. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 678-685. doi: 10.4153/CJM-1974-064-9
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