Another theorem he helped to establish shows that analytic functions of several variables can be applied in the general setting of Banach algebras.
32.
His areas of research involve representation theory, C *-algebra characterizations, the notion of an approximate identity in a Banach algebra, and Banach bundle theory.
33.
Bade's research started out in operator theory, but he soon moved into Banach algebras where he made fundamental contributions to the field of automatic continuity.
34.
The exponential function also has analogues for which the argument is a matrix, or even an element of a Banach algebra or a Lie algebra.
35.
The study of rings that are not necessarily commutative is known as noncommutative algebra; it includes ring theory, representation theory, and the theory of Banach algebras.
36.
In slightly more abstract language, the holomorphic functional calculus can be extended to any element of a Banach algebra, using essentially the same arguments as above.
37.
The commutative Banach algebra and Hardy space " H " & infin; consists of the bounded holomorphic functions on the open unit disc " D ".
38.
By the Fubini Tonelli theorem, the convolution is submultiplicative with respect to the L ^ 1 norm, making L ^ 1 ( G ) a Banach algebra.
39.
In 1956 Naimark published his monograph " Normed Rings ", which gave the first comprehensive treatment of Banach algebras, and was enormously influential in the development of the field.
40.
Appl . article with Turkish authors that is citation number 1 in the article, and Glickfeld, Barnett W ., The theory of analytic functions in commutative Banach algebras with involution.
