Related papers: Stability of derivations under weak-2-local contin…

Let H be a separable Hilbert space with a fixed orthonormal basis (e_n), n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators T: H -> H. Identifying l^\infty = C(\beta N) with the diagonal operators, we consider…

Let $p\in(0,\frac{N}{N-2\alpha})$, $\alpha\in(0,1)$ and $\Omega\subset \R^N$ be a bounded $C^2$ domain containing $0$. If $\delta_0$ is the Dirac measure at $0$ and $k>0$, we prove that the weakly singular solution $u_k$ of $(E_k)$ $…

We construct the weak nonstandard hull of a normed linear space X from *X (the nonstandard extension of X) using the weak topology on X. The bidual (i.e. the second dual) X" is shown to be isometrically isomorphic to the weak nonstandard…

We prove some $L^{\infty}$ a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of $C^n$ and on compact K\"ahler manifolds. We also show optimal $L^p$…

A precise description of the injective envelope of a spatial continuous trace C*-algebra A over a Stonean space Delta is given. The description is based on the notion of a weakly continuous Hilbert bundle, which we show to be a…

In this paper, we establish a regularity results for weak solutions of Robin problems driven by the well-known Orlicz $g$-Laplacian operator. Precisely, by using a suitable variation of the Moser iteration technique, we prove that every…

Let $A$ be a $C^*$-algebra, $H$ be a Hilbert $A$-module and $K(H)$ be the closure of the set of finite rank module maps. We show that the $W^*$-algebra of all bounded $A^{**}$-module maps on the smallest self-dual Hilbert $A^{**}$-module…

For a compact Hausdorff space $X$, the space $SC(X\times X)$ of separately continuous complex valued functions on $X$ can be viewed as a $C^*$-subalgebra of $C(X)^{**}\overline\otimes C(X)^{**}$, namely those elements which slice into…

We consider Dirichlet problems for linear elliptic equations of second order in divergence form on a bounded or exterior smooth domain $\Omega$ in $\mathbb{R}^n$, $n \ge 3$, with drifts $\mathbf{b}$ in the critical weak $L^n$-space…

We prove that every biorthogonality preserving linear surjection between two dual or compact C$^*$-algebras or between two von Neumann algebras is automatically continuous.

We define the notion of $\varphi$-perturbation of a densely defined adjointable mapping and prove that any such mapping $f$ between Hilbert ${\mathcal A}$-modules over a fixed $C^*$-algebra ${\mathcal A}$ with densely defined corresponding…

In this work, we describe local and 2-local $\frac12$-derivations of infinite-dimensional Lie algebras. We prove that all local and 2-local $\frac12$-derivations of the Witt algebra as well as of the positive Witt algebra and the classical…

We study the regularity of weak solutions to a certain class of second order parabolic system under the only assumption of continuous coefficients. By using the $A-$caloric approximation argument, we claim that the weak solution $u$ to such…

We present a proof of the local H\"older regularity of the horizontal derivatives of weak solutions to the $p$-Laplace equation in the Heisenberg group $\mathbb{H}^1$ for $p>4 $.

For any $n\ge 2$, $\Omega\subset\rn$, and any given convex and coercive Hamiltonian function $H\in C^{0}(\rn)$, we find an optimal sufficient condition on $H$, that is, for any $c\in\mathbb R$, the level set $H^{-1}(c)$ does not contains…

We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples of finite-dimensional nilpotent Lie algebras $\mathcal{L}$…

This paper initiates the study of 2-local derivations on Lie algebras over fields of prime characteristic. Let $\mathfrak{g}$ be a simple Jacobson-Witt algebra $W_n$ over a field of prime characteristic $p$ with cardinality no less than…

In this paper we study derivations in subalgebras of $L_{0}^{wo}(\nu ;% \mathcal{L}(X)) $, the algebra of all weak operator measurable funtions $f:S\to \mathcal{L}(X) $, where $% \mathcal{L}(X) $ is the Banach algebra of all bounded linear…

We study the regularity of weak solutions for two elliptic systems involving the $n$-Laplacian and a critical nonlinearity in the right hand side: $H$-systems and $n$-harmonic maps into compact Riemannian manifolds. Under the assumptions…

Let $\A$ be a $C^*$-algebra and $\B$ be a von Neumann algebra that both act on a Hilbert space $\Ha$. Let $\M$ and $\N$ be inner product modules over $\A$ and $\B$, respectively. Under certain assumptions we show that for each mapping…