11. Unital Banach algebras over the complex field provide a general setting to develop spectral theory. 12. BV ( \ Omega ) "'respect to each argument, making this function space a Banach algebra . 13. The quaternions are also an example of a composition algebra and of a unital Banach algebra . 14. The theory of real Banach algebras can be very different from the theory of complex Banach algebras. 15. The theory of real Banach algebras can be very different from the theory of complex Banach algebras . 16. C *-algebras, which are Banach algebras with some additional structure, play an important role in quantum mechanics. 17. If is a compact Hausdorff space, then the maximal ideal space of the Banach algebra is homeomorphic to. 18. Much of the foregoing discussion can be set in the more general context of a complex Banach algebra . 19. There are a number of other fields, such as Banach algebra theory, that draw on several complex variables. 20. In every Banach algebra with multiplicative identity, the set of invertible elements forms a topological group under multiplication.
