The basic mathematical framework for super Hilbert spaces over a Graßmann algebra with a Graßmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Graßmann algebras arise in the functional Schrödinger representation of spinor quantum field theory in a natural way. a email: [email protected]

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.

This manuscript explores a new class of non-autonomous second-order stochastic inclusions Clarke?s subdifferential form with non-instantaneous impulses (NIIs), unbounded delay, and the Rosenblatt process in Hilbert spaces. The existence solution is deduced by employing fixed point strategy for set-valued map together evolution operator analysis approach. An example analyzed theoretical developm...

Some reverses of the continuous triangle inequality for Bochner integral of vectorvalued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ-mixing condition.

We use the fixed point alternative theorem to prove that, under suitable conditions, every A-valued approximate isometry on a Hilbert C∗-module over the C∗-algebra A can be approximated by a unique A-valued isometry. AMS subject classifications: Primary 39B52, 39B82, 46B04, 46L08; Secondary 47H10

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

In this paper, we introduce some gap functions for set-valued mixed variational inequalities under suitable conditions. We further use these gap functions to study global error bounds for the solutions of set-valued mixed variational inequalities in Hilbert spaces. The results presented in this paper generalize and improve some corresponding known results in literatures.