English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let A be a Banach algebra, X a closed subspace of A∗, Y a dual Banach space with predual Y∗, and π a continuous representation of A on Y. We call π subordinate to X if each coordinate function πy,λ ∈ X, for all y ∈ Y, λ ∈ Y∗. If X is topologically left (right) introverted and Y is reflexive, we show the existence of a natural bijection between continuous representations of A on Y subordinate to X, and normal representations of X∗ on Y. We show that if A has a bounded approximate identity, then every weakly almost periodic functional on A is a coordinate function of a continuous representation of A subordinate to WAP(A). We show that a function f on a locally compact group G is left uniformly continuous if and only if it is the coordinate function of the conjugate representation of L1(G), associated to some unitary representation of G. We generalize the latter result to an arbitrary Banach algebra with bounded right approximate identity. We prove the functionals in LUC(A) are all coordinate functions of some norm continuous representation of A on a dual Banach space.

Representations of Banach algebras subordinate to topologically introverted spaces