相关论文: Various notions of point derivations in Banach alg…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…
This article focuses on a new concept of quadratic variation for processes taking values in a Banach space $B$ and a corresponding covariation. This is more general than the classical one of M\'etivier and Pellaumail. Those notions are…
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
Several recent papers investigated unbounded versions of order and norm convergences in Banach lattices. In this paper, we study the unbounded variant of weak convergence and its relationship with other convergences. In particular, we…
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
The use of the properties of actions on an algebra to enrich the study of the algebra is well-trodden and still fashionable. Here, the notion and study of endomorphic elements of (Banach) algebras are introduced. This study is initiated, in…
We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…
In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a…
We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different…
In this paper, we study Jordan derivation-like maps on the $\theta-$Lau products of algebras. We characterize them and prove that under certain condition any Jordan derivation-like maps on the $\theta-$Lau products is a derivation-like map.…
For $m\geq 2$, we study derivations on symbol algebras of degree $m$ over fields with characteristic not dividing $m$. A differential central simple algebra over a field $k$ is split by a finitely generated extension of $k$. For certain…
These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.
In this paper we study decompositions and classification problems for unbounded derivations in Bunce-Deddens-Toeplitz and Bunce-Deddens algebras. We also look at implementations of these derivations on associated GNS Hilbert spaces.
The existence of multiple fixed points for the coercive, bilinear, compact forms defined in the cone in the Banach space. Multiple applications to the integral equations derived from BVPs for differential equations are provided.
The aim of this note is to consider different notions for the Banach-Saks property in locally solid vector lattices as an extension for the known concepts of the Banach-Saks property in Banach lattices. We investigate relations between…
There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and…
We study random unconditional convergence for a basis in a Banach space. The connections between this notion and classical unconditionality are explored. In particular, we analyze duality relations, reflexivity, uniqueness of these bases…
Introducing the notions of (inner) $\sigma$-derivation, (inner) $\sigma$-endomorphism and one-parameter group of $\sigma$-endomorphisms ($\sigma$-dynamics) on a Banach algebra, we correspond to each $\sigma$-dynamics a $\sigma$-derivation…