ABSTRACT
Banach Algebra Inequalities If X is a Banach algebra then for all x, y ∈ B
||xy|| ≤ ||x|| ||y||.
Comments (i) This is the defining inequality for a topological algebra that is a Banach space; for a definition see: Norm Inequalities Comments (i). (ii) For particular cases see: Bounded Variation Function Inequalities (b),
references [EM, vol. 1, pp. 329-332]; Hewitt & Stromberg [HS, pp. 83-84].
Barnes’s Inequalities (a) If a, b are non-negative concave n-tuples, a increasing and b decreasing, then
