52 research outputs found
The Shilov boundary for a -analog of the holomorphic functions on the unit ball of symmetric matrices
We describe the Shilov boundary for a -analog of the algebra of
holomorphic functions on the unit ball in the space of symmetric
matrices.Comment: 14 page
Beurling-Fourier Algebras and Complexification
In this paper, we develop a new approach that allows to identify the Gelfand
spectrum of weighted Fourier algebras as a subset of an abstract
complexification of the corresponding group for a wide class of groups and
weights. This generalizes some recent results of
Ghandehari-Lee-Ludwig-Spronk-Turowska on the spectrum of Beurling-Fourier
algebras on some Lie groups. In the case of discrete groups we consider a more
general concept of weights and classify them in terms of finite subgroups.Comment: 40 page
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
Operator synthesis II. Individual synthesis and linear operator equations
The second part of our work on operator synthesis deals with individual
operator synthesis of elements in some tensor products, in particular in
Varopoulos algebras, and its connection with linear operator equations. Using a
developed technique of ``approximate inverse intertwining'' we obtain some
generalizations of the Fuglede and the Fuglede-Weiss theorems. Additionally, we
give some applications to spectral synthesis in Varopoulos algebras and to
partial differential equations.Comment: 42 page
Shilov boundary for "holomorphic functions" on a quantum matrix ball
We describe the Shilov boundary ideal for a q-analog of algebra of
holomorphic functions on the unit ball in the space of matrices.Comment: 14 page
On bounded and unbounded idempotents whose sum is a multiple of the identity
We study bounded and unbounded representations of the -algebra
generated by idempotents whose sum equals
(, is the identity)
Operator synthesis. I. Synthetic sets, bilattices and tensor algebras
The interplay between the invariant subspace theory and spectral synthesis
for locally compact abelian group discovered by Arveson is extended to include
other topics as harmonic analysis for Varopoulos algebras and approximation by
projection-valued measures. We propose a ''coordinate'' approach which
nevertheless does not use the technique of pseudo-integral operators, as well
as a coordinate free one which allows to extend to non-separable spaces some
important results and constructions of [W.Arveson, Operator Alegebras and
Invariant subspaces, Ann. of Math. (2) 100 (1974)] and solve some problems
posed there.Comment: 32 pages. to appear in Journal of Functional Analysi
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
- …