Related papers: Complex Vector Lattices Via Functional Completions
We study completions of Archimedean vector lattices relative to any nonempty set of positively-homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric closed…
Suppose E and F are locally convex-solid vector lattices. Although we have a suitable vector lattice structure for the tensor product E and F (known as the Fremlin tensor product and denoted by E\otimesF), there is a lack of topological…
Suppose $\Sigma$ is a topological space and $S(\Sigma)$ is the vector lattice of all equivalent classes of continuous real-valued functions defined on open dense subsets of $\Sigma$. In this paper, we establish some lattice and topological…
Kang et al. provided a path realization of the crystal graph of a highest weight module over a quantum affine algebra, as certain semi-infinite tensor products of a single perfect crystal. In this paper, this result is generalized to give a…
Given an Archimedean vector lattice $E$, we present one elementary property of $E$ which is equivalent to the entire traditional list of axioms which makes $E$ a $\Phi$-algebra. We call a vector lattice with this property ``square closed".…
In this paper, we characterize when, for any infinite cardinal {\alpha}, the Fremlin tensor product of two Archimedean Riesz spaces is Dedekind {\alpha}-complete. We also provide an example of an ideal I in an Archimedean Riesz space E such…
Let $F/F_0$ be a quadratic extension of totally real number fields, and let $E$ be an elliptic curve over $F$ which is isogenous to its Galois conjugate over $F_0$. A quadratic extension $M/F$ is said to be almost totally complex (ATC) if…
A representational approach to constructing the Fremlin tensor product of two Archimedean Riesz spaces. [Warning: do not view the HTML version!]
It is known that there are complete, Hausdorff and regular convergence vector spaces X and Y such that Lc(X,Y), the space of continuous linear mappings from X into Y equipped with the continuous convergence structure, is not complete. In…
In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism $Conc(A \otimes B)\cong Conc A \otimes Conc B$, holds, provided that the tensor product satisfies a very natural condition (of being…
On a class of compact Hermitian manifolds including compact K\"{a}hler manifolds, we prove that the the relative non-pluripolar product is always well-defined. We also prove the monotonicity of the relative non-pluripolar product in terms…
First, we define some concepts similar to the local compactoidity or the c-compactness, and study relationships between these concepts and the original ones. As a result, we find a characterization of the local compactoidity when its…
We prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient…
We derive an explicit expression for an associative star product on non-commutative versions of complex Grassmannian spaces, in particular for the case of complex 2-planes. Our expression is in terms of a finite sum of derivatives. This…
The set of f-vectors of pure simplicial complexes is an important but little understood object in combinatorics and combinatorial commutative algebra. Unfortunately, its explicit characterization appears to be a virtually intractable…
The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…
A convenient technique for calculating completed topological tensor products of functional Frechet and DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…
The truncation operation facilitates the articulation and analysis of several aspects of the structure of archimedean vector lattices; we investigate two such aspects in this article. We refer to archimedean vector lattices equipped with a…
We study completeness of a topological vector space with respect to different filters on the set N of all naturals. In the metrizable case all these kinds of completeness are the same, but in non-metrizable case the situation changes. For…
We prove an identity for sesquilinear maps from the Cartesian square of a vector space to a geometric mean closed Archimedean (real or complex) vector lattice, from which the Cauchy-Schwarz inequality follows. A reformulation of this result…