This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: >_ 0 for v e LP([O,=);V (p>2) with v(t) e K a.e. in [0,=), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V ...

We investigate symmetry properties of vector-valued diffusion and Schrödinger equations. For a separable Hilbert space H we characterize the subspaces of L2 R3 ;H that are local i.e., defined pointwise and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symme...

We propose a stochastic Forward Douglas-Rachford Splitting framework for finding a zero point of the sum of three maximally monotone operators in real separable Hilbert space, where one of them is cocoercive. We first prove the weak almost sure convergence of the proposed method. We then characterize the rate of convergence in expectation in the case of strongly monotone operators. Finally, we ...

We show the existence result of viable solutions to the differential inclusion ẋ(t) ∈ G(x(t)) + F (t, x(t)) x(t) ∈ S on [0, T ], where F : [0, T ] × H → H (T > 0) is a continuous set-valued mapping, G : H → H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) ⊂ ∂g(x), where g : H → R is a regular and locally Lipschitz function and S is a ball, compact subset in a separable H...

A new techniques for proving the existence of fixed points of groups of isometric transformations is developed. It is used to find simpler proofs and real-case versions of previous results of the authors. In particular, we use the obtained fixed point theorem to show that a bounded representation in a separable, real or complex, Hilbert space which has an invariant indefinite quadratic form wit...

Let H be a (separable) Hilbert space and {ek}k≥1 a fixed orthonormal basis of H. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis. This is used to refine previous work on scaled projections, and to obtain a new characteri...

An inclusion of observable nets satisfying duality induces an inclusion of canonical field nets. Any Bose net intermediate between the observable net and the field net and satisfying duality is the fixed– point net of the field net under a compact group. This compact group is its canonical gauge group if the occurrence of sectors with infinite statistics can be ruled out for the observable net ...

This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H , and of families of maps on B(H). It is shown that the a one parameter group is uniformly equicontinuous if and only if the group of unitaries which implements it is so. A “geometrical” necessary and sufficient condition is given for a family of operators to be uniformly equicontinuous.

This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H , and of families of maps on B(H). It is shown that a one parameter group of automorphisms is uniformly equicontinuous if and only if the group of unitaries which implements it is so. A “geometrical” necessary and sufficient condition is given for a family of operators to be uniformly equicontinuous.