Projective Limits in Harmonic Analysis

Proposition Algebra with Projective Limits

Sequential logic deviates from propositional logic by taking into account that atomic propositions yield different Boolean values at different times during the sequential evaluation of a single proposition. Reactive valuations capture this dynamics of a proposition’s environment. This logic is phrased as an equationally specified algebra rather than in the form of proof rules. It is strictly mo...

On strong liftings for projective limits

We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called “self-consistency”, which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies. In...

On Prohorov's Criterion for Projective Limits

Representations of Topological Algebras by Projective Limits

It is shown that a) it is possible to define the topology of any topological algebra by a collection of F -seminorms, b) every complete locally uniformly absorbent (complete locally A-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of metrizable locally uniformly absorbent algebras (respectively, A-(k-normed) algebras, where k ∈ (0, 1] varies, c) every complete...

Projective limits of topological vector spaces