Bounded and unitary elements in pro-C^*-algebras

A pro-C^*-algebra is a (projective) limit of C^*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C^*-algebras can be seen as non-commutative k-spaces. An element of a pro-C^*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C^*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C^*-algebra. In this paper, we investigate pro-C^*-algebras from a categorical point of view. We study the functor (-)_b that assigns to a pro-C^*-algebra the C^*-algebra of its bounded elements, which is the dual of the Stone-\v{C}ech-compactification. We show that (-)_b is a coreflector, and it preserves exact sequences. A generalization of the Gelfand-duality for commutative unital pro-C^*-algebras is also presented.Comment: v2 (accepted

Investigations of Epitaxial Ga : YIG(111) Films by Brillouin Light Scattering and Microwave Spectroscopy

Brillouin light scattering and microwave spectroscopy measurements have enabled the room temperature magnetic characteristics of five Y3Fe5-xGaxO12(111) films with 0≤x≤0.73 to be obtained. The film thicknesses ranged from 7 to 10 microns. The BLS measurements gave stiffness factors ranging from 5.52 to 8.77.10-9 Oe.cm2. This variation is attributed to the occupation by Ga atoms of the A and D sites causing a decrease in Jad. The values of 4πMs, and γ deduced were in good agreement with those obtained by microwave spectroscopy which examined the frequencies of the MSBVW and MSFVW excitations generated by a periodic array of microstrips. 4πMs decreased from 1.740 kG for x = 0 to 0.645 kG for x = 0.73. A cubic anisotropy field HK of ~45 Oe and first and second order uniaxial anisotropy fields Hu1 and Hu2 of ~-70 and 50 Oe respectively were obtained