Smooth operators in the commutant of a contraction

• Autorzy: Pascale Vitse
• Języki publikacji: EN

Abstrakty

EN

For a completely non-unitary contraction T, some necessary (and, in certain cases, sufficient) conditions are found for the range of the $H^{∞}$ calculus, $H^{∞}(T)$, and the commutant, {T}', to contain non-zero compact operators, and for the finite rank operators of {T}' to be dense in the set of compact operators of {T}'. A sufficient condition is given for {T}' to contain non-zero operators from the Schatten-von Neumann classes $S_{p}$.

Kategorie tematyczne

• 47A45: Canonical models for contractions and nonselfadjoint operators
• 47A60: Functional calculus
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 47A20: Dilations, extensions, compressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 3
• Strony: 241-263

Daty

wydano

2003

Twórcy

autor

Pascale Vitse

• Department of Mathematics and Statistics, Laval University, Québec, Canada G1K 7P4

Identyfikatory

DOI

10.4064/sm155-3-4