We give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-ideal in a Hilbert algebra and we prove a separation theorem. We also define the concept of semi-h...

This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...

For a standard graded algebra R, we consider embeddings of the poset of Hilbert functions of R-ideals into the poset of R-ideals, as a way of classification of Hilbert functions. There are examples of rings for which such embeddings do not exist. We describe how the embedding can be lifted to certain ring extensions, which is then used in the case of polarization and distraction. A version of a...

In this paper, we introduce a notion of strongly quasi-local algebras. They are defined for each discrete metric space with bounded geometry, and sit between the Roe algebra quasilocal algebra. We show that algebras coarse invariants, hence encoding geometric information underlying spaces. prove geometry which admits embedding into Hilbert space, inclusion induces an isomorphism in $K$-theory.

Abstract The problem of finding generators the subalgebra invariants under action a group automorphisms finite-dimensional Lie algebra on its universal enveloping is reduced to homogeneous same acting symmetric tensor algebra. This process applied prove constructive Hilbert–Nagata Theorem (including degree bounds) for in nilpotent relatively free associative endowed with an induced by represent...

Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2-planar algebra capturing the structure contained in the double complex pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system. We now introduce the notion of modules over an A2-planar algebra, and describe certain irreducible Hilbert A2-TL-modules. We construct an A2-graph planar algeb...

In a recent paper by Hirzallah et al. [O. Hirzallah, F. Kittaneh, M. Krnić, N. Lovričević, and J. Pečarić. Eigenvalue inequalities for differences of means of Hilbert space operators. Linear Algebra and its Applications, 436:1516–1527, 2012.], several eigenvalue inequalities are obtained for the difference of weighted arithmetic and weighted geometric means of two positive invertible operators ...

The purpose of this chapter is to write about Quot and Hilbert functors and to prove that these are algebraic spaces provided certain technical conditions are satisfied. In this chapter we will discuss this in the setting of algebraic space. A reference is Grothendieck’s lectures, see [Gro95a], [Gro95b], [Gro95e], [Gro95f], [Gro95c], and [Gro95d]. Another reference is the paper [OS03]; this pap...

We study the Hilbert polynomials of non-standard graded algebras R, that are finitely generated on generators not all of degree one. Given an expression P (R, t) = a(t)/(1 − t) for the Poincaré series of R as a rational function, we study for 0 ≤ i ≤ l the graded subspaces ⊕kRkl+i (which we denote R[l; i]) of R, in particular their Poincaré series and Hilbert functions. For example, we prove th...

A C* algebra is a closed self-adjoint subalgebra of B(H), the bounded operators on a Hilbert space H. Kirchberg asked whether every C* algebra embeds into an ultrapower of a particular C* algebra, the Cuntz algebra O_2. In this talk, I will explain the model-theoretic content of this problem. In particular, I will show how model-theoretic forcing can be used to give a weak local reformulation o...