2,137 research outputs found
On the connection between sets of operator synthesis and sets of spectral synthesis for locally compact groups
We extend the results by Froelich and Spronk and Turowska on the connection
between operator synthesis and spectral synthesis for A(G) to second countable
locally compact groups G. This gives us another proof that one-point subset of
G is a set of spectral synthesis and that any closed subgroup is a set of local
spectral synthesis. Furthermore we show that ``non-triangular'' sets are strong
operator Ditkin sets and we establish a connection between operator Ditkin sets
and Ditkin sets. These results are applied to prove that any closed subgroup of
is a local Ditkin set.Comment: 21 page
The C*-algebras of connected real two-step nilpotent Lie groups
Using the operator valued Fourier transform, the C*-algebras of connected
real two-step nilpotent Lie groups are characterized as algebras of operator
fields defined over their spectra. In particular, it is shown by explicit
computations, that the Fourier transform of such C*-algebras fulfills the norm
controlled dual limit property.Comment: 37 pages, submitted to "Revista Matem\'atica Complutense
Beurling-Fourier algebras on compact groups: spectral theory
For a compact group we define the Beurling-Fourier algebra
on for weights defined on the dual \what G and taking positive
values. The classical Fourier algebra corresponds to the case is the
constant weight 1. We study the Gelfand spectrum of the algebra realizing it as
a subset of the complexification defined by McKennon and
Cartwright and McMullen. In many cases, such as for polynomial weights, the
spectrum is simply . We discuss the questions when the algebra
is symmetric and regular. We also obtain various results concerning spectral
synthesis for .Comment: 37 page
- …