A Real p-Homogeneous Seminorm with Square Property Is Submultiplicative

A real seminorm with square property is submultiplicative

A Seminorm with Square Property on a Complex Associative Algebra Is Submultiplicative

The result stated in the title is proved as a consequence of an appropriate generalization replacing the square property of a seminorm with a similar weaker property which implies an equivalence to the supnorm of all continuous functions on a compact Hausdorff space also. Theorem. Let p be a seminorm with the square property on a complex (associative) algebra A. Then the following hold for all ...

Standard deviation is a strongly Leibniz seminorm

We show that standard deviation σ satisfies the Leibniz inequality σ(fg) ≤ σ(f)‖g‖ + ‖f‖σ(g) for bounded functions f, g on a probability space, where the norm is the supremum norm. A related inequality that we refer to as “strong” is also shown to hold. We show that these in fact hold also for noncommutative probability spaces. We extend this to the case of matricial seminorms on a unital C*-al...

The relaxed square property

Graph products are characterized by the existence of non-trivial equivalence relations on the edge set of a graph that satisfy a so-called square property. We investigate here a generalization, termed RSP-relations. The class of graphs with non-trivial RSP-relations in particular includes graph bundles. Furthermore, RSP-relations are intimately related with covering graph constructions. For K2,...

Nonassociative Algebras with Submultiplicative Bilinear Form

In this paper algebras with identity, over ordered fields, which possess a (weak) submultiplicative positive bilinear form are studied. They are called (weak) subdecomposition algebras. It is proved that every weak subdecomposition algebra is a simple quadratic algebra with no nontrivial nilpotents or idempotents. If a weak subdecomposition algebra is also flexible, then it is a noncommutative ...