Conversion from nonstandard matrix algebras to standard factors of type $\mathrm{II}_{1}$

Conversion from Nonstandard to Standard Measure Spaces and Applications in Probability Theory

Let (X, 3, v) be an internal measure space in a denumerably comprehensive enlargement. The set X is a standard measure space when equipped with the smallest standard o-algebra % containing the algebra a, where the extended real-valued measure p. on % is generated by the standard part of v. If / is fl-measurable, then its standard part / is jR-measurable on X. If / and p. are finite, then the vi...

- Algebras and Nonstandard Analysis

Suppose B is an ultraproduct of finite dimensional C∗-algebras. We consider mapping and injectability properties for separable C∗algebras into B. In the case of approximately finite C∗-algebras, we obtain a classification of these mappings up to inner conjugacy. Using a Theorem of Voiculescu, we show that for nuclear C ∗-algebras injectability into an ultraproduct of finite dimensional C ∗-alge...

Algebras from Standard Constructions

Conversion from vacuum to standard air wavelengths

We explore possible expressions for the conversion between vacuumwavelengths and wavelengths in standard air. We find that the equation proposed in the SDSS website is not appropriate for APOGEE. The differences between the available approximations in the H band are at the level of a fraction of a milliAngstroms, or several meters per second, and a significant contribution is related to the cha...

NILPOTENT GRAPHS OF MATRIX ALGEBRAS

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...