1. CJM 2016 (vol 69 pp. 434)
 | Lee, Hun Hee; Youn, Sang-gyun
 |
New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups
In this paper we introduce a new way of deforming convolution
algebras and Fourier algebras on locally compact groups. We demonstrate
that this new deformation allows us to reveal some information
of the underlying groups by examining Banach algebra properties
of deformed algebras. More precisely, we focus on representability
as an operator algebra of deformed convolution algebras on compact
connected Lie groups with connection to the real dimension of
the underlying group. Similarly, we investigate complete representability
as an operator algebra of deformed Fourier algebras on some finitely
generated discrete groups with connection to the growth rate
of the group.
Keywords:Fourier algebra, convolution algebra, operator algebra, Beurling algebra Categories:43A20, 43A30, 47L30, 47L25 |
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2. CJM 2016 (vol 69 pp. 54)
 | Hartz, Michael
 |
On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces
We continue the investigation of the isomorphism problem for
multiplier algebras of reproducing kernel
Hilbert spaces with the complete Nevanlinna-Pick property.
In contrast to previous work in this area,
we do not study these spaces by identifying them with restrictions
of a universal space, namely the Drury-Arveson space.
Instead, we work directly with the Hilbert spaces and their
reproducing kernels. In particular,
we show that two multiplier algebras of Nevanlinna-Pick spaces
on the same set are equal if and only if the Hilbert
spaces are equal. Most of the article is devoted to the study
of a special class of
complete Nevanlinna-Pick spaces on homogeneous varieties. We
provide a complete
answer to the question of when two multiplier algebras of spaces
of this type
are algebraically or isometrically isomorphic. This generalizes
results of Davidson, Ramsey, Shalit,
and the author.
Keywords:non-selfadjoint operator algebras, reproducing kernel Hilbert spaces, multiplier algebra, Nevanlinna-Pick kernels, isomorphism problem Categories:47L30, 46E22, 47A13 |
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3. CJM 2009 (vol 61 pp. 1239)
 | Davidson, Kenneth R.; Yang, Dilian
 |
Periodicity in Rank 2 Graph Algebras
Kumjian and Pask introduced an aperiodicity condition
for higher rank graphs.
We present a detailed analysis of when this occurs
in certain rank 2 graphs.
When the algebra is aperiodic, we give another proof
of the simplicity of $\mathrm{C}^*(\mathbb{F}^+_{\theta})$.
The periodic $\mathrm{C}^*$-algebras are characterized, and it is shown
that $\mathrm{C}^*(\mathbb{F}^+_{\theta}) \simeq
\mathrm{C}(\mathbb{T})\otimes\mathfrak{A}$
where $\mathfrak{A}$ is a simple $\mathrm{C}^*$-algebra.
Keywords:higher rank graph, aperiodicity condition, simple $\mathrm{C}^*$-algebra, expectation Categories:47L55, 47L30, 47L75, 46L05 |
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