We prove a Banach version of Garland's method proving vanishing cohomology for groups acting on simplicial complexes. The novelty this new is that our condition applies to every reflexive space. This allows us deduce several criteria group with coefficients in classes spaces (uniformly curved spaces, Hilbertian and $L^p$ spaces). Using these criteria, we improve recent results regarding fixed p...

Let k be a field of characteristic different from 2. Let E/k be a finite separable extension with a k-linear involution σ. For every σ-symmetric element μ ∈ E∗, we define a hermitian scaled trace form by x ∈ E 7→ TrE/k(μxx). If μ = 1, it is called a hermitian trace form. In the following, we show that every even-dimensional quadratic form over a hilbertian field, which is not isomorphic to the ...

We introduce a new class of spatial Cox processes driven by Hilbert-valued random log-intensity. adopt parametric framework in the spectral domain, to estimate its functional correlation structure. Specifically, we consider functional, approach based on periodogram operator, inspired Whittle estimation methodology. Strong consistency estimator is proved linear case. illustrate this property sim...

We investigate the distribution of eigenvalues of completely nuclear maps on an operator space. We prove that eigenvalues of completely nuclear maps are square-summable in general and summable if the underlying operator space is Hilbertian and homogeneous. Conversely, if eigenvalues are summable for all completely nuclear maps, then every finite dimensional subspace of the underlying operator s...

We present geometric methods for uniformly discretizing the N -qubit Hilbert space, producing the equivalent of the Platonic solids in 2 dimensional Hilbert space. The group of transformations leaving these uniform Hilbertian polytopes invariant known as the Clifford group provides a general language for describing discrete transformations on N qubits. Our geometric approach to discretization s...

December 22, 1999 Abstract. Suppose A is a hyperfinite von Neumann algebra with a normal faithful normalized trace τ . We prove that if E is a homogeneous Hilbertian subspace of Lp(τ) (1 ≤ p < ∞) such that the norms induced on E by Lp(τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous Hilberti...