Geodesic
Smooth operators in the commutant of a contraction
Pascale Vitse1
1 Department of Mathematics and Statistics Laval University Québec, Canada G1K 7P4
Studia Mathematica, Tome 155 (2003) no. 3, pp. 241-263

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $S_p$.
DOI : 10.4064/sm155-3-4
Keywords: completely non unitary contraction necessary certain cases sufficient conditions found range infty calculus infty commutant contain non zero compact operators finite rank operators dense set compact operators sufficient condition given contain non zero operators schatten von neumann classes nbsp

Pascale Vitse 1

1 Department of Mathematics and Statistics Laval University Québec, Canada G1K 7P4 
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Pascale Vitse. Smooth operators in the commutant of a contraction. Studia Mathematica, Tome 155 (2003) no. 3, pp. 241-263. doi: 10.4064/sm155-3-4

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