Related papers: Bounded depth in Hilbert algebras

Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 - \epsilon) n. On the other hand, there is a frame which does not contain bases with…

We examine Hilbert bimodules which possess a (generally unbounded) involution. Topics considered include a linking algebra representation, duality, locality, and the role of these bimodules in noncommutative differential geometry.

We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for…

The second part of the Hilbert's sixteenth problem consists in determining the upper bound $\mathcal{H}(n)$ for the number of limit cycles that planar polynomial vector fields of degree $n$ can have. For $n\geq2$, it is still unknown…

Let $S_n=K[x_1,\ldots,x_n,y]$ and $I_n=(x_1y,x_2y,\ldots,x_ny)\subset S_n$ be the edge ideal of star graph. We prove that $\operatorname{hdepth}(S_n/I_n)\geq \left\lceil \frac{n}{2} \right\rceil + \left\lfloor \sqrt{n} \right\rfloor - 2$.…

Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…

Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful…

This article introduces Hilbert $*$-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linear maps. Other examples include…

Engel subalgebras of finite-dimensional Leibniz algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that a left Leibniz algebra, all of whose maximal subalgebras are right ideals, is nilpotent. A…

We give two algorithms for computing the Hilbert depth of a \emph{graded ideal} in the polynomial ring. These algorithms work efficiently for (squarefree) lex ideals. As a consequence, we construct counterexamples to some conjectures made…

We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information…

We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…

By contrast wih $\mathsf{S4}$, the analysis of local tabularity above $\mathsf{IPC}$ has provided a difficult challenge. This paper studies a strengthening of local tabularity -- \textit{uniform local tabularity} -- where one demands that…

We show that several reducts of Heyting polyadic algebras of infinite dimension, with and without equality enjoy various amalgamation properties. In the equality free case we obtain superamalgamation, but when we have equality we obtain a…

Stanley decompositions of multigraded modules $M$ over polynomials rings have been discussed intensively in recent years. There is a natural notion of depth that goes with a Stanley decomposition, called the Stanley depth. Stanley…

The main purpose of this paper is to study the finite-dimensional solvable Lie algebras described in its title, which we call {\em minimal non-${\mathcal N}$}. To facilitate this we investigate solvable Lie algebras of nilpotent length $k$,…

Necessary and sufficient conditions for a dense subspace of a Hilbert space to be a linear Hilbertian manifold domain are given. Some relations between linear Hilbertian manifold domains and domains of self-adjoint operators are found.

In this paper we discuss, in terms of quivers with relations, sufficient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension two and we give a sufficient condition for it to be…

Let $\mathbf m=(x_1,\ldots,x_n)$ be the maximal graded ideal of $S:=K[x_1,\ldots,x_n]$. We present a new method for computing the Hilbert depth of powers of $\mathbf m$.

Let $R$ be a positively graded algebra over a field. We say that $R$ is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical…