We study the complexification of real Hilbert C∗-modules over real C∗-algebras. We give an example of a Hilbert Ac-module that is not the complexification of any Hilbert A-module, where A is a real C∗-algebra.

We explain the precise relationship between two module-theoretic descriptions of sheaves on an involutive quantale, namely the description via so-called Hilbert structures on modules and that via so-called principally generated modules. For a principally generated module satisfying a suitable symmetry condition we observe the existence of a canonical Hilbert structure. We prove that, when worki...

The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product H⊗̂H is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C∗-algebra is shown to be completely bounded with ‖b‖cb = ‖b‖. The so ca...

We construct classes of von Neumann algebra modules by considering “column sums” of noncommutative Lp spaces. Our abstract characterization is based on an Lp/2-valued inner product, thereby generalizing Hilbert C*-modules and representations on Hilbert space. While the (single) representation theory is similar to the L2 case, the concept of Lp bimodule (p 6= 2) turns out to be nearly trivial.

We consider a homogenization problem associated with quasi-crystalline multiple integrals of the form $u_\varepsilon\in L^p(\Omega;\mathbbm{R}^d) \mapsto \int_\Omega f_R(x,\frac{x}{\varepsilon}, u_\varepsilon(x)), dx,$ where \(u_ǎrepsilon) is subject to constant-coefficient linear partial differential constraints. The structure underlying composite encoded in dependence on second variable Lagra...

Geometric Representation Theory for semi-simple Lie groups has two main sheaf theoretic models. Namely, through Beilinson-Bernstein localization theory, Harish-Chandra modules are related to holonomic sheaves of D modules on the flag variety. Then the (algebraic) Riemann-Hilbert correspondence relates these sheaves to constructible sheaves of complex vector spaces. On the other hand, there is a...