Linearly equivalent topologies and locally quasi-unmixed rings

Locally Quasi-Convex Compatible Topologies on a Topological Group

For a locally quasi-convex topological abelian group (G, τ), we study the poset C (G, τ) of all locally quasi-convex topologies on G that are compatible with τ (i.e., have the same dual as (G, τ)) ordered by inclusion. Obviously, this poset has always a bottom element, namely the weak topology σ(G, Ĝ). Whether it has also a top element is an open question. We study both quantitative aspects of ...

Locally Linearly Dependent Operators

Let T be a linear operator defined on a complex vector space X and let n be a positive integer. Kaplansky [4] proved that T is algebraic of degree at most n if and only if for every x ∈ X the vectors x, Tx, . . . , Tnx are linearly dependent. One consequence of Kaplansky’s result is that if X is a Banach space and T : X → X a bounded linear operator, then T is algebraic if and only if for every...

Quasi-Primitive Rings and Density Theory

Locally compact linearly Lindelöf spaces

There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel’skii and Buzyakova.

Locally ̂ - Equivalent Algebras ^ )

Let A be a Banach "-algebra. A is locally ¿"-equivalent if, for every selfadjoint element t e A, the closed *-subalgebra of A generated by / is *-isomorphic to a ¿"-algebra. In this paper it is shown that when A is locally ¿"-equivalent, and in addition every selfadjoint element in A has at most countable spectrum, then A is *-isomorphic to a ¿"-algebra.