Hadamard Determinant Inequality with Wigner Theorem and Convergent Star Products on Hilbert Spaces

Abstract

The Jenson operator inequality and for spectral order with submajorization, transformations on the set of all n-dimensional subspaces of a Hilbert space, orthogonality and in metric-projective geometry are discussed. The complete positivity of Rieffel deformation quantization by actions of the Euclidean space and nuclear Weyl algebra are presented. The Fuglede-Kadison and Hadamard determinants and inequalities with determinants of perturbed positive matrices and extensions in operators on Hilbert space are characterized. We show the isometries and the geometric version of Wigner theorem on Grassmann spaces and for Hilbert Grassmannians. We investigate C^*-completion, the DFR-algebra and the convergent star products for the projective limits of Hilbert spaces.