Related papers: Natural generalized invertibility and prescribed i…
Skew idempotent functionals of ordered semirings are studied. Different associative and non-associative semirings are considered. Theorems about properties of skew idempotent functionals are proved. Examples are given.
For a class of singular Sturm-Liouville equations on the unit interval with explicit singularity $a(a + 1)/x^2, a \in \mathbb{N}$, we consider an inverse spectral problem. Our goal is the global parametrization of potentials by spectral…
In this paper, we investigate the converse of the Tan-Xu theorem, which states that the naturally reductive property of a Riemannian metric is inherited by a naturally reductive $(\alpha_1,\alpha_2)$-metric, and we show that, under certain…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
Rao and Mitra in 1972 introduced two different types of constraints to extend the concept of Bott-Duffin inverse and defined a new constrained inverse. Mary in 2011 defined the inverse along an element that generalizes the Moore-Penrose and…
Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In a general setting they can be described as frame multipliers, consisting of analysis, multiplication by…
The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed $L^0$-modules (in the sense of Gigli) over a metric measure space.
Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove…
We study coherent $I$-indexed algebras and associated noncommutative projective schemes, where the index set $I$ is a locally finite directed poset. Our main result is a characterisation of such noncommutative projective schemes in terms of…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
In this note devoted to some aspects of the inverse problem of representation theory the attention is concentrated on the interrelations between various algebraic structures (algebras with operators) unraveled by different solutions of the…
The induction and reduction precesses of an O*-vector space $\M$ obtained by means of a projection taken, respectively, in $\M$ itself or in its weak bounded commutant $\M'_\w$ are studied. In the case where $\M$ is a partial GW*-algebra,…
In this paper we characterize invertible matrices over an arbitrary commutative antiring S and find the structure of GL_n (S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every…
We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective…
Let $K$ be an {\em arbitrary} field of characteristic $p>0$, let $A$ be one of the following algebras: $P_n:= K[x_1, ..., x_n]$ is a polynomial algebra, $\CD (P_n)$ is the ring of differential operators on $P_n$, $\CD (P_n)\t P_m$, the…
We describe algorithms for computing the induced nilpotent orbits in semisimple Lie algebras. We use them to obtain the induction tables for the Lie algebras of exceptional type. This also yields the classification of the rigid nilpotent…
In this paper, necessary and sufficient conditions are given for the existence of Moore-Penrose inverse of a product of two matrices in an indefinite inner product space (IIPS) in which reverse order law holds good. Rank equivalence…
In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame…
In the late 1980s, A. Premet conjectured that the variety of nilpotent elements of any finite dimensional restricted Lie algebra over an algebraically closed field of characteristic $p>0$ is irreducible. This conjecture remains open, but it…
The spectral properties of Dirac operators on $(0,1)$ with potentials that belong entrywise to $L_p(0,1)$, for some $p\in[1,\infty)$, are studied. The algorithm of reconstruction of the potential from two spectra or from one spectrum and…