This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involut ...
Let k be a field of characteristic ≠2, A be a central simple algebra with involution σ over k and W(A,σ) be the associated Witt group of hermitian forms. We prove that for all purely inseparable extensions L of k, the canonical map rL/k:W(A,σ)⟶W(AL,σL) is ...
We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operato ...
Let G be a locally compact group and H a closed amenable subgroup of G. We prove that every element in A(p)(H) with compact support can be extended to an element of A(p)(G) of which we control the norm and support. The result is new even for the Fourier al ...
Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamen ...