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.

A new, numerical framework for the approximation of solutions to matrix-valued Riemann–Hilbert problems is developed, based on a recent method for the homogeneous Painlevé II Riemann–Hilbert problem. We demonstrate its effectiveness by computing solutions to other Painlevé transcendents. An implementation in Mathematica is made available online.

We develop a white noise framework for Lévy processes on Hilbert spaces. As the main result of this paper, we then employ these white noise techniques to explicitly represent strong solutions of stochastic differential equations driven by a Hilbert-space-valued Lévy process.

We introduce the Hilbert space-valued Wiener process and the corresponding stochastic integral of Itô type. This is then used together with semigroup theory to obtain existence and uniqueness of weak solutions of linear and semilinear stochastic evolution problems in Hilbert space. Finally, this abstract theory is applied to the linear heat and wave equations driven by additive noise.

Existence of invariant measures for semi-linear stochastic evolution equations in separable real Hilbert spaces is considered, where the noise is generated by Hilbert space valued Lévy processes. It is shown that if the Lévy process has locally bounded second moments, if the semigroup generated by the linear part is hyperbolic, and if the Lipschitz constants of the nonlinearities are sufficient...

Let M be a Banach C*-module over a C*-algebra A carrying two A-valued inner products 〈., .〉1, 〈., .〉2 which induce equivalent to the given one norms on M. Then the appropriate unital C*-algebras of adjointable bounded A-linear operators on the Hilbert A-modules {M, 〈., .〉1} and {M, 〈., .〉2} are shown to be ∗-isomorphic if and only if there exists a bounded A-linear isomorphism S of these two Hi...

by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

* Correspondence: fuquanxia@sina. com Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, P. R. China Full list of author information is available at the end of the article Abstract In this paper, a projective splitting method for solving a class of generalized mixed variational inequalities is considered in Hilbert spaces. We investigate a general iterative algorithm...

In this paper, we considered a Stochastic Interval-Valued Linear Fractional Programming problem(SIVLFP). In this problem, the coefficients and scalars in the objective function are fractional-interval, and technological coefficients and the quantities on the right side of the constraints were random variables with the specific distribution. Here we changed a Stochastic Interval-Valued Fractiona...

We show that every scalar valued continuous function f(g) on a compact group G may be written as f(g) = 〈Φ(g)ξ, η〉 for all g ∈ G, where ξ, η are vectors in a separable Hilbert space H, and Φ(g) is a strongly continuous unitary valued function on G which is a product of unitary representations and antirepresentations of G on H. This product is countable, but always converges uniformly on G. More...