Vector lattices and \(f\)-algebras: the classical inequalities. (English) Zbl 1397.46001

Buskes, G.; Schwanke, C.

Banach J. Math. Anal. 12, No. 1, 191-205 (2018).

Three famous inequalities are proved in some important connections: the Cauchy-Schwarz inequality, the Hölder inequality, and the Minkowski inequality. The authors work in vector spaces over the field of real or complex numbers, and some Archimedean vector lattices over the field.

Reviewer: Beloslav Riečan (Banská Bystrica)

MSC:

46A40

Ordered topological linear spaces, vector lattices

Keywords:

vector lattice; \(f\)-algebra; Cauchy-Schwarz inequality; Hölder inequality; Minkowski inequality