The norm on X and on B(X) the Banach algebra
of all bounded linear operators acting on X, will be denoted by [parallel] * [paralle].
To be able to apply methods from the theory of Banach algebras
to the solution of those problems, it is essential to determine if a class of linear operators of a sequence space X into itself is a Banach algebra
; this is nontrivial if X is a BK space that does not have AK.
A painstakingly precise keeper of numbers - as a math prof, he wrote a two-volume, 1,617-page book on Banach algebra
- Palmer has spreadsheets that shows he spent 8.
Let (X, [parallel]*[parallel]) be a Banach space and let B(X) be the Banach algebra
of all linear and bounded operators acting from X into X.
Let B(H) denote the Banach algebra
of all bounded linear operators on a Hilbert space H.
Every ([alpha], [phi])-approximate strongly higher derivation in a Banach algebra
is a higher derivation.
2] is called a Banach algebra
homomorphism if it is also multiplicative, i.
In , the present author investigated hypergeometric and basic hypergeometric series involving noncommutative parameters and argument (short: noncommutative hypergeometric series, and noncommutative basic or Q-hypergeometric series) over a unital ring R (or, when considering nonterminating series, over a unital Banach algebra
R) from a different, nevertheless completely elementary, point of view.
A Banach algebra
structure for the Wiener algebra W(D) of the disc.
Several of his appendices also offer independent interest, covering amenable groups, Banach algebra
, bundles of C*-algebras, groups, representations of C*-algebras, direct integrals, Effros's ideal center decomposition, the Fell topology.
Additionally, in the papers just mentioned, the localization condition is generalized so that the cross-Gramian matrices of localized frames belong to a particular Banach algebra
Among his topics are elements of measure theory, a Hilbert space interlude, linear transformations, locally convex spaces, and Banach algebras
and spectral theory.