Smooth operators in the commutant of a contraction

Pascale Vitse. "Smooth operators in the commutant of a contraction." Studia Mathematica 155.3 (2003): 241-263. <http://eudml.org/doc/286162>.

@article{PascaleVitse2003,
abstract = {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 $S_\{p\}$.},
author = {Pascale Vitse},
journal = {Studia Mathematica},
keywords = {Hilbert space contraction; compact operators; functional calculus; Schatten-von Neumann classes; commutant lifting theorem},
language = {eng},
number = {3},
pages = {241-263},
title = {Smooth operators in the commutant of a contraction},
url = {http://eudml.org/doc/286162},
volume = {155},
year = {2003},
}

TY - JOUR
AU - Pascale Vitse
TI - Smooth operators in the commutant of a contraction
JO - Studia Mathematica
PY - 2003
VL - 155
IS - 3
SP - 241
EP - 263
AB - 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 $S_{p}$.
LA - eng
KW - Hilbert space contraction; compact operators; functional calculus; Schatten-von Neumann classes; commutant lifting theorem
UR - http://eudml.org/doc/286162
ER -