Gaussian elements in CCR algebras
arXiv:1908.10428
Abstract
A system of matrix units in the Weyl algebra of convolution type is constructed with the aid of a Gaussian element so that it includes von Neumann's minimal projection, which explicitly shows that the associated C*-algebra is a compact operator algebra. The spectral decomposition of an arbitrary Gaussian element is then worked out in terms of the diagonal projections in the matrix units.
10 pages, minor corrections with one reference added