Related papers: Combinatorial algorithms for binary operations on …
In this paper, we propose methods for computing the Hilbert series of multigraded right modules over the free associative algebra. In particular, we compute such series for noncommutative multigraded algebras. Using results from the theory…
We briefly discuss linear algebraic, combinatorial, and applied aspects of an exact model representation of binary arrays. As an illustration, we present two linear algebraic portraits of a string of characters.
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…
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…
In this paper, we establish some basic properties of certain operators (element of centroids, averaging operators, derivations, Nijenhuis operators, Rota-Baxter operators) on (compatible) ternary Leibniz algebras and give the classification…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
The so-called Sasaki projection was introduced by U. Sasaki on the lattice L(H) of closed linear subspaces of a Hilbert space H as a projection of L(H) onto a certain sublattice of L(H). Since L(H) is an orthomodular lattice, the Sasaki…
We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore,…
We extend the operations of shorting and parallel addition from the cone of bounded nonnegative selfadjoint operators in a Hilbert space to the set of all nonnegative selfadjoint linear relations. New properties of these operations and…
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…
This is the sixth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VI), we construct the appropriate…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
When ${\cal{D}}$ is a linear partial differential operator of any order, a direct problem is to look for an operator ${\cal{D}}_1$ generating the compatibility conditions (CC) ${\cal{D}}_1\eta=0$ of ${\cal{D}}\xi=\eta$. We may thus…
We construct a localization for operads with respect to one-ary operations based on the Dwyer-Kan hammock localization. For an operad O and a sub-monoid of one-ary operations W we associate an operad LO and a canonical map O to LO which…