Details

Autor(en) / Beteiligte

• Bakonyi, Mihály
• Woerdeman, Hugo J

Titel

Contractive analogs

Ist Teil von

• Matrix Completions, Moments, and Sums of Hermitian Squares, 2011, Vol.37, p.257-360

Ort / Verlag

United States: Princeton University Press

Erscheinungsjahr

2011

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• An operator$T \in \mathcal{L}(\mathcal{H},\mathcal{H}')$is called acontractionif ∥T∥ ≤ 1, and astrict contractionif ∥T∥ < 1. In this chapter we deal with contractive completions of partial operator matrices. Since the norm of a submatrix is always less or equal to the norm of the matrix itself, every partial matrix which admits a contractive completion has to bepartially contractive(or apartial contraction), that is, all its fully specified submatrices are contractions. A contractive completion problem can always be reduced to a positive semidefinite one. That is because Lemma 2.4.4 implies that ∥T∥ ≤ 1 if and only