A survey of the Kreiss matrix theorem for power bounded families of matrices and its extensions. (English) Zbl 0877.15029

Strikwerda, John C.; Wade, Bruce A.

Janas, Jan (ed.) et al., Linear operators. Proceedings of the semester organized at the Stefan Banach International Mathematical Center, Warsaw, Poland, February 7–May 15, 1994. Warsaw: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 38, 339-360 (1997).

Summary: We survey results related to the Kreiss matrix theorem, especially examining extensions of this theorem to Banach space and Hilbert space. The survey includes recent and established results together with proofs of many of the interesting facts concerning the Kreiss matrix theorem.
For the entire collection see [Zbl 0863.00036].

MSC:

15A60

Norms of matrices, numerical range, applications of functional analysis to matrix theory

Keywords:

power-bounded families of matrices; Kreiss matrix theorem; Banach space; Hilbert space