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We give two characterisations of tracially nuclear C*-algebras. The first is that the finite summand of the second dual is hyperfinite. The second is in terms of a variant of the weak* uniqueness property. The necessary condition holds for all tracially nuclear C*-algebras. When the algebra is separable, we prove the sufficiency.
α-Bi2O3 thin films were deposited on different substrates by atomic layer deposition method. The results of X-ray diffraction, high-resolution transmission electron microscopy and X-ray photoelectron spectroscope correspond to α-Bi2O3. The Fourier transform infrared spectroscopy analyses indicate that the reaction is rather complete during the deposition. Optical properties of the films have been investigated using ultraviolet-infrared transmittance spectra in the temperature range of 8–300 K. It is found that the band gap Eg decreases from 3.12 to 3.03 eV with the temperature. The parameters αB and ΘB of the Bose-Einstein model are 69.3 meV and 293.9 K, respectively. The band narrowing coefficient dEg/dT is −0.435 meV/K at room temperature. The present results can be considerable for future application of Bi2O3-based electro-optic and wide temperature range optoelectronic devices.
In the paper, we introduce a new concept, topological orbit dimension of an
-tuple of elements in a unital
-algebra. Using this concept, we conclude that Voiculescu's topological free entropy dimension of every finite family of self-adjoint generators of a nuclear
-algebra is less than or equal to 1. We also show that the Voiculescu's topological free entropy dimension is additive in the full free product of some unital
-algebras. We show that the unital full free product of Blackadar and Kirchberg's unital
algebras is also an
algebra. As an application, we obtain that
is not a group.
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