Related papers: Closure operators on algebras
In this paper, we study the operator equation $AB=\lambda BA$ for a bounded operator $A,B$ on a complex Hilbert space. We focus on algebraic relations between different operators that include normal, $M$-hyponormal, quasi $*$-paranormal and…
We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.
In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of…
We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notion…
We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…
The notion of $\mathcal{O}$-operators on modules over Lie algebras generalize Rota-Baxter operators. They also generalize Poisson structures on Lie algebras in the presence of modules. Motivated from Poisson structures, we define gauge…
In this short note, we provide OPEs for several affine W-algebras associated with Lie algebras of rank two and give some direct applications.
The purpose of this paper is to study algebras of singular integral operators on $\mathbb{R}^{n}$ and nilpotent Lie groups that arise when one considers the composition of Calder\'on-Zygmund operators with different homogeneities, such as…
The present paper deals with complemented lattices where, however, a unary operation of complementation is not explicitly assumed. This means that an element can have several complements. The mapping $^+$ assigning to each element $a$ the…
For associative commutative algebras $A$ with Rota-Baxter operator $R$ identities of the algebra $AR=(A,\circ)$, where $a\circ b= aR(b),$ are found.
We involve a certain propositional logic based on ortholattices. We characterize the implicational reduct of such a logic and we show that its algebraic counterpart is the so-called orthosemilattice. Properties of congruences and congruence…
Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is…
In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert…
We consider varieties generated by finite closure algebras whose canonical relations have two levels, and whose restriction to a level is an "extremal" relation, i.e. the identity or the universal relation. The corresponding logics have…
Starting from the operator algebra of the (1+1)D Ising model on a spatial lattice, this paper explicitly constructs a subalgebra of smooth operators that are natural candidates for continuum fields in the scaling limit. At the critical…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
An expansive, monotone operator is dominating; if it is also idempotent it is a closure operator. Although they have distinct properties, these two kinds of discrete operators are also intertwined. Every closure operator is dominating;…