We consider algebra bundles where the fibre is an algebra of bounded operators in a separable Hilbert space H over the complex numbers. If the Hilbert space H is infinite dimensional, the algebra is either ℬ the algebra of all bounded operators on H or K the algebra of compact operators in ℬ, and we refer to these bundles as operator algebra bundles. If the Hilbert space H is finite dimensional, the algebra is just the n 2-dimensional matrix algebra M n (C), and we refer to these bundles as matrix algebra bundles.
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Husemöller, D., Joachim, M., Jurčo, B., Schottenloher, M. (2008). Isomorphism Classification of Operator Algebra Bundles. In: Basic Bundle Theory and K-Cohomology Invariants. Lecture Notes in Physics, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74956-1_19
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