Alternatively, the continuous calculus can be obtained via the Gelfand transform, in the context of commutative Banach algebras.
22.
This follows from the fact that, if " A " is a complex Banach algebra, the resolvent function ).
23.
Mazur made important contributions to geometrical methods in linear and nonlinear functional analysis and to the study of Banach algebras.
24.
In other words, the only complex Banach algebra that is a division algebra is the complex numbers "'C " '.
25.
*PM : Neumann series in Banach algebras, id = 9756 new !-- WP guess : Neumann series in Banach algebras-- Status:
26.
*PM : Neumann series in Banach algebras, id = 9756 new !-- WP guess : Neumann series in Banach algebras-- Status:
27.
The central theorem can now be proved by Banach algebra methods, and contains much, though not all, of the previous theory.
28.
The advent of Wiener's tauberian theorem marked an epoch in the subject, introducing unexpected connections to Banach algebra methods in Fourier analysis.
29.
An affinoid algebra is a " k "-Banach algebra that is isomorphic to a quotient of the Tate algebra by an ideal.
30.
For example, in a unital *-Banach algebra, the closed unit ball is contained in the closed convex hull of the unitary elements.
