Details of talk
|Title||Cwikel estimates in noncommutative plane|
|Presenter||Galina Levitina (University of New South Wales)|
|Session||Geometry and Topology|
One of the most beautiful results in operator theory are the so-called Cwikel estimates concerning the singular values of the operator $M_f g(-i\nabla)$ on $L_2(R^d)$, where $M_f$ denotes the multiplication operator by the function $f$ and $\nabla$ denotes the gradient. Several analogues of Cwikel estimates have been proved for different spectral triples in noncommutative geometry, where they represent an important tool in identification of the dimension of a locally compact spectral triple. In our joint work with F. Sukochev (UNSW) and D. Zanin (UNSW) we propose a new approach in the definition of noncommutative plane (also known as the Moyal plane). Using this new definition we significantly improve Cwikel estimates for noncommutative plane previously proved by Gayral, Iochum, and V\'arilly.