We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let A be a Banach algebra and X a Banach A-module, f : X → X and g : A → A. The mappings Δ1 f,g , Δ2 f,g , Δ3 f,g , and Δ4 f,g are defined and it is proved that if ‖Δ1 f,g x, y, z,w ‖ resp., ‖Δ3 f,g x, y, z,w, α, β ‖ is dominated by φ x, y, z,w , then f is a generalized re...

a celebrated result of i. schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the theory of groups. in this paper we exhibit a similar result to schur's theorem for vector spaces, acted upon by certain groups. the proof of this analogous result depends on the characteristic o...

In this paper we characterize the left Jordan derivations on Banach algebras. Also, it is shown that every bounded linear map $d:mathcal Ato mathcal M$ from a von Neumann algebra $mathcal A$ into a Banach $mathcal A-$module $mathcal M$ with property that $d(p^2)=2pd(p)$ for every projection $p$ in $mathcal A$ is a left Jordan derivation.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

The articles [22], [5], [3], [2], [4], [6], [21], [16], [14], [15], [1], [17], [19], [20], [7], [8], [9], [12], [11], [10], and [13] provide the terminology and notation for this paper. For simplicity we adopt the following rules: x is arbitrary, R is an associative ring, V is a left module over R, v, v1, v2 are vectors of V , A, B are subsets of V , and l is a linear combination of A. We now d...

A recent development in data-driven modelling addresses the problem of identifying dynamic models of interconnected systems, represented as linear dynamic networks. For these networks the notion network identifiability has been introduced recently, which reflects the property that different network models can be distinguished from each other. Network identifiability is extended to cover the uni...

for two algebras $a$ and $b$, a linear map $t:a longrightarrow b$ is called separating, if $xcdot y=0$ implies $txcdot ty=0$ for all $x,yin a$. the general form and the automatic continuity of separating maps between various banach algebras have been studied extensively. in this paper, we first extend the notion of separating map for module case and then we give a description of a linear separa...