On Stability of Polynomially Bounded Operators

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2007
• ISSN: 1812-9471
• Main Authors: Muraz, G., Quoc Phong Vu
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106447
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Stability of Polynomially Bounded Operators азвание / G. Muraz, Quoc Phong Vu // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 234-240. — Бібліогр.: 13 назв. — англ.

We prove that if T is a polynomially bounded operator and the peripheral spectrum of T has zero measure, then Tⁿx → 0 for all x in X if and only if T* has no nontrivial invariant subspace on which it is invertible and doubly power bounded.