Norms on unitizations of banach algebras revisited

Let A be an algebra without unit. If ∥ ∥ is a complete regular norm on A it is known that among the regular extensions of ∥ ∥ to the unitization of A there exists a minimal (operator extension) and maximal (ℓ₁-extension) which are known to be equivalent. We shall show that the best upper bound for the ratio of these two extensions is exactly 3. This improves the results represented by A. K. Gaur and Z. V. Kovářík and later by T. W. Palmer. The second author was partially supported by the grant No. 201/03/0041 of GAČR.     

Non unital locally uniformlyA-p-convex algebras

The unitization of a locally uniformlyA-p-convex algebra is not always of the same type. In non unitary ones, we exhibit a strongerm-p-convex topology, which plays the role of ap-norm in the unitary case. Some structure results are given, while we also supply hints to clarify the aforesaid phenomenon.     

THE EFFECT OF MONOPSONY POWER ON PRORATIONING AND UNITIZATION REGULATION OF THE COMMON POOL

For four decades beginning in the 1930s, the U.S. oil and gas industry was regulated by a quota‐supported price‐floor instrument known as prorationing. Most economists argue that unitization would have been a more efficient form of regulation. This paper studies how monopsony power held by integrated pipeline/refinery firms affects that conclusion. Absent regulation, the underproduction by monopsony dominates the overproduction from common‐property supply. Thus, unitization, which forces producers to internalize costs, causes output to be further restricted. In contrast, prorationing severs the price‐setting ability of the monopsonist, so can increase output to the first‐best. Under prorationing, at the first‐best output level, the marginal monopsony rents equal the Pigouvian output tax that solves the common‐property problem. Also discussed are the distribution of gains under prorationing and unitization as implemented.