Bilinear forms on $H\sp{\infty }$ and bounded bianalytic functions

A note on bilinear forms

Bilinear Forms on Frobenius Algebras

We analyze the homothety types of associative bilinear forms that can occur on a Hopf algebra or on a local Frobenius k-algebra R with residue field k. If R is symmetric, then there exists a unique form on R up to homothety iff R is commutative. If R is Frobenius, then we introduce a norm based on the Nakayama automorphism of R. We show that if two forms on R are homothetic, then the norm of th...

Bilinear Forms

The geometry of Rn is controlled algebraically by the dot product. We will abstract the dot product on Rn to a bilinear form on a vector space and study algebraic and geometric notions related to bilinear forms (especially the concept of orthogonality in all its manifestations: orthogonal vectors, orthogonal subspaces, and orthogonal bases). Section 1 defines a bilinear form on a vector space a...

Quadratic APN functions as subspaces of alternating bilinear forms

In this note we illuminate and apply the equivalence of quadratic APN functions to certain subspaces of alternating bilinear forms. These subspaces can be characterized by the rank-distance of the dual subspace, or equivalently , as the subspaces of 2 F m 2 avoiding the variety of elements of rank 2. Or, in the geometric language, as subspaces external (or skew) to the line Grassmannian.

Arens regularity of bilinear forms and unital Banach module spaces

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...