Projections In L1(G): The Unimodular Case

• We consider the issue of describing all self-adjoint idempotents (projections) in L1(G) when G is a unimodular locally compact group. The approach is to take advantage of known facts concerning subspaces of the Fourier-Stieltjes and Fourier algebras of G and the topology of the dual space of G. We obtain an explicit description of any projection in L1(G) which happens to also lie in the coefficient space of a finite direct sum of irreducible representations. This leads to a complete description of all projections in L1(G) for G belonging to a class of groups that includes SL2(R) and all second countable almost connected nilpotent locally compact groups.

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

L1-projection

locally compact group

unimodular

square-integrable representation.

square-integrable representation.

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)