| Softcover ISBN: | 978-2-85629-971-5 |
| Product Code: | SMFMEM/177 |
| List Price: | $65.00 |
| AMS Member Price: | $52.00 |
| Softcover ISBN: | 978-2-85629-971-5 |
| Product Code: | SMFMEM/177 |
| List Price: | $65.00 |
| AMS Member Price: | $52.00 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 177; 2023; 186 ppMSC: Primary 46; 43; 47
The authors introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative \(L^{p}\)-space. They equally prove that two classical operator norms, the regular norm and the decomposable norm, are identical.
The authors also describe precisely the regular norm of several classes of regular multipliers. This includes Schur multipliers and Fourier multipliers on some unimodular locally compact groups that can be approximated by discrete groups in various senses. A main ingredient is to show the existence of a bounded projection from the space of completely bounded \(L^{p}\)operators onto the subspace of Schur or Fourier multipliers, preserving complete positivity.
On the other hand, the authors show the existence of bounded Fourier multipliers that cannot be approximated by regular operators, on large classes of locally compact groups, including all infinite abelian locally compact groups. The authors finish by introducing a general procedure for proving positive results on self-adjoint contractively decomposable Fourier multipliers, beyond the amenable case.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
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The authors introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative \(L^{p}\)-space. They equally prove that two classical operator norms, the regular norm and the decomposable norm, are identical.
The authors also describe precisely the regular norm of several classes of regular multipliers. This includes Schur multipliers and Fourier multipliers on some unimodular locally compact groups that can be approximated by discrete groups in various senses. A main ingredient is to show the existence of a bounded projection from the space of completely bounded \(L^{p}\)operators onto the subspace of Schur or Fourier multipliers, preserving complete positivity.
On the other hand, the authors show the existence of bounded Fourier multipliers that cannot be approximated by regular operators, on large classes of locally compact groups, including all infinite abelian locally compact groups. The authors finish by introducing a general procedure for proving positive results on self-adjoint contractively decomposable Fourier multipliers, beyond the amenable case.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
