Smooth operators in the commutant of a contraction
Tom 155 / 2003
Studia Mathematica 155 (2003), 241-263
MSC: 47A45, 47A60, 47B10, 47A20.
DOI: 10.4064/sm155-3-4
Streszczenie
For a completely non-unitary contraction $T$, some necessary (and, in certain cases, sufficient) conditions are found for the range of the $ H^{\infty} $ calculus, $ H^{\infty} (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 $S_p$.
