The Riemann sphere of a commutative Banach algebra

Elements in a Commutative Banach Algebra Determining the Norm Topology

For an element a of a commutative complex Banach algebra (A, ‖ · ‖) we investigate the following property: every complete norm | · | on A making the multiplication by a from (A, | · |) to itself continuous is equivalent to ‖ · ‖.

Commutative Algebra Commutative Algebra : General

Weak amenability of (2N)-th dual of a Banach algebra

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.

Rotations of the Riemann Sphere

The set Rot(S) of such rotations forms a group, most naturally viewed as a subgroup of GL3(R). Showing this requires some linear algebra. Recall that if m ∈ M3(R), meaning that m is a 3-by-3 real matrix, then its transpose m is obtained by flipping about the diagonal. That is, mij = mji for i, j = 1, 2, 3. The transpose is characterized by the more convenient condition 〈mx, y〉 = 〈x,my〉 for all ...

Structure of Certain Banach Algebra Products

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.