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 [14], 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.