On the algebraic closure in rings
The "algebraic closure" of a subset K C A of a ring is an algebraic analogue of topological closure.
Thin spectra and stable range conditions
Abstract The topological stable rank of a Banach algebra A is the least integer n = tsr(A) such that Un(A) is dense in An, where Un(A) = {(a1,…, an) ϵ An: ∑i = 1nAai = A}. We give a spectral characterization of the condition “tsr(A) ⩽ n,” valid for arbitrary Banach algebras. For a commutative Banach algebra A, the condition tsr(A) ⩾ n is related to the presence of some kind of discs in the spectrum X(A).
FURUTA INEQUALITY AND ITS RELATED TOPICS
This article is devoted to a brief survey of Furuta inequality and its related topics. It consists of 4 sections: 1. From Lowner-Heinz inequality to Furuta inequality, 2. Ando-Hiai inequality, 3. Grand Furuta inequality, and 4. Chaotic order.