In this paper, we show that every separable simple tracially approximately divisible C ? $C^*$ -algebra has strict comparison, and it is either purely infinite or stable rank one. As a consequence, (non-unital) finite Z ${\cal Z}$ -stable

We construct a simple C∗-algebra with nuclear dimension zero that is not isomorphic to its tensor product with the Jiang–Su algebra Z, and a hyperfinite II1 factor not isomorphic to its tensor product with the separable hyperfinite II1 factor R. The proofs use a weakening of the Continuum Hypothesis. Elliott’s program of classification of nuclear (a.k.a. amenable) C∗-algebras recently underwent...

We consider the algebra $\dot\Sigma(\mathcal L)$ generated by inner-limit derivations over ${\rm GICAR}$ of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to lattice, we demonstrate that image $\dot \Sigma(\mathcal through Fock representation can be completed gro...

We prove by elementary methods the following generalization of a theorem due to Gleason, Kahane, and Żelazko. Let A be a real algebra with unit 1 such that the spectrum of every element in A is bounded and let φ : A→ C be a linear map such that φ(1) = 1 and (φ(a))2 + (φ(b))2 = 0 for all a, b in A satisfying ab = ba and a2 + b2 is invertible. Then φ(ab) = φ(a)φ(b) for all a, b in A. Similar resu...

Three southern USA forestry species, loblolly pine (Pinus taeda), Virginia pine (Pinus virginiana), and shortleaf pine (Pinus echinata), were previously shown to be spectrally separable (83% accuracy) using data from a full-range spectroradiometer (400–2500 nm) acquired above tree canopies. This study focused on whether these same species are also separable using hyperspectral data acquired usi...

Let X be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of C(X)-algebras by C(X)subalgebras with controlled complexity. The following applications are given. All unital separable continuous fields of C*-algebras over X with fibers isomorphic to a fixed Cuntz algebra On, n ∈ {2, 3, ...,∞} are locally trivial....

Given a conjugation C on separable complex Hilbert space H, bounded linear operator T H is said to be C-skew symmetric if CTC = -T*. This paper describes the maps, algebra of all operators acting that preserve difference for every H.

(1) A Frobenius algebra in a tensor category C is an abstract algebracoalgebra where (co)multiplication and (co)unit are arrows in C. A Frobenius extension A|S may be viewed as a Frobenius algebra in the category M of S-bimodules under ordinary tensor product over S, as described in connection with corings in NEFE, chapter 4. The notion of a special Frobenius algebra in a category is a basic no...