Abstract. Let θ : M → N be a zero-product preserving linear map between algebras. We show that under some mild conditions θ is a product of a central element and an algebra homomorphism. Our result applies to matrix algebras, standard operator algebras, C * -algebras and W * -algebras.

Abstract. The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points F (S) of a nonexpansive mapping S and the set of solutions Ω A of the variational inequality for a monotone, Lipschitz continuous mapping A. We introduce a hybrid extragradient-like approximation method which is based on the well-known extragradient method and a hybrid (or outer approximation) method. The method produces three sequences which are shown to converge strongly to the same common element of F (S) ∩ Ω A . As applications, the method provides an algorithm for finding the common fixed point of a nonexpansive mapping and a pseudocontractive mapping, or a common zero of a monotone Lipschitz continuous mapping and a maximal monotone mapping.

In this paper, we prove that into isometries and disjointness preserving linear Ž . Ž . maps from C X into C Y are essentially weighted composition operators 0 0Tf s h и f ( for some continuous map and some continuous scalar-valued function h. ᮊ

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Let C be a closed convex subset of a real Hilbert space H. Let A be an inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H such that the domain of B is included in C. We introduce two iteration schemes of finding a point of (A + B) −1 0, where (A + B) −1 0 is the set of zero points of A + B. Then, we prove two strong convergence theorems of Halpern's type in a Hilbert space. Using these results, we get new and well-known strong convergence theorems in a Hilbert space.

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This article extends the tensor network Kalman filter to matrix outputs with an application in recursive identification of discrete-time nonlinear multiple-input-multiple-output (MIMO) Volterra systems. This extension completely supersedes previous work, where only l scalar outputs were considered. The Kalman tensor equations are modified to accommodate for matrix outputs and their implementation using tensor networks is discussed. The MIMO Volterra system identification application requires the conversion of the output model matrix with a row-wise Kronecker product structure into its corresponding tensor network, for which we propose an efficient algorithm. Numerical experiments demonstrate both the efficacy of the proposed matrix conversion algorithm and the improved convergence of the Volterra kernel estimates when using matrix outputs.

In this paper, we consider equilibrium problems and introduce the concept of (S) + condition for bifunctions. Existence results for equilibrium problems with the (S) + condition are derived. As special cases, we obtain several existence results for the generalized nonlinear variational inequality studied by Ding and Tarafdar [12], and the generalized variational inequality studied by Cubiotti and Yao [11], respectively. Finally, applications to a class of eigenvalue problems are given. In particular, we derive an existence result for this class of eigenvalue problems where the parameter does not need to be restricted to bounded intervals and the operator is not needed to be bounded.