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Olof Giselsson

Publications and source records attributed to Olof Giselsson.

10 recordsLinked to original sources
arXiv2026

Multipliers of Beurling-Fourier algebras

For a locally compact group G we introduce and study the reduced Beurling-Fourier-Stieltjes algebra, a weighted analogue of the reduced Fourier-Stieltjes algebra, together with the algebra of completely bounded multipliers of the associated weighted Fourier algebra. We show, in particular, that these two algebras coincide when G is amenable. For a general locally compact group G, we identify them as subspaces of the reduced Fourier-Stieltjes algebra and of the space of functions that locally belong to the Fourier algebra, respectively. Furthermore, we establish sufficient conditions on the group and the weight under which the algebra of completely bounded multipliers of the weighted Fourier algebra embeds into its unweighted counterpart.

math.FA↗
arXiv2025

Cartan subproduct systems

Given a semisimple compact Lie group $G$ and a nonzero dominant integral weight $\lambda$, the highest weight $G_q$-modules $V_{n\lambda}$ form a subproduct system of finite dimensional Hilbert spaces. Using a conjectural asymptotic behavior of Clebsch-Gordan coefficients we identify the corresponding Cuntz-Pimsner algebras with algebras of quantized functions on homogeneous spaces of $G$. We also show that the gauge-invariant part of the Toeplitz algebra provides a model for convergence of full matrix algebras to quantum flag manifolds, complementing and generalizing results of Landsman and Rieffel for $q=1$ and results of Vaes-Vergnioux in the rank one case for $q\ne1$. We verify our conjecture on Clebsch-Gordan coefficients for $G=SU(n)$ and all weights that are either regular or multiples of the fundamental weight $\omega_1$. For $\lambda=\omega_1$, we also provide a detailed description of the Toeplitz and Cuntz-Pimsner algebras, generalizing results of Arveson on symmetric subproduct systems.

math.OA↗
arXiv2023

Quantum $SU(3)$ as the $C^*$-algebra of a 2-graph

We show that for $q\in (0,1),$ the $C^{*}$-algebra $SU_{q}(3)$ is isomorphic a rank $2$ graph $C^{*}$-algebra (in the sense of Pask and Kumjian). This graph is derived by passing the to the limit $q\to 0$ for a set of generators of $SU_{q}(3)$. Moreover, the isomorphism can be taken to be $\mathbb{T}^{2}$-equivariant with respect the right-action on $SU_{q}(3)$ and the gauge action coming from the $2$-graph

math.OA↗
arXiv2020

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 recent related results of Ghandehari-Lee-Ludwig-Spronk-Turowska (Adv. Math. 2021) about the spectrum of Beurling-Fourier algebras on some Lie groups. In the case of discrete groups we show that the spectrum of Beurling-Fourier algebra is homeomorphic to $G$.

math.FA↗
arXiv2018

q-Independence of the Jimbo-Drinfeld Quantization

Let $\mathrm G$ be a connected semi-simple compact Lie group and for $0<q<1$, let $(\mathbb{C}[\mathrm{G]_q}],\Delta_q)$ be the Jimbo-Drinfeld $q$-deformation of $\mathrm G$. We show that the $C^*$-completions of $\mathrm{C}[\mathrm{G]_q}$ are isomorphic for all values of $q$. Moreover, these isomorphisms are equivariant with respect to the right-action of the maximal torus.

math.QA↗
arXiv2018

The Universal $C^*$-Algebra of the Quantum Matrix Ball and its Irreducible $*$-Representations

We prove that any irreducible $*$-representation of $\mathrm{Pol}(\mathrm{Mat}_n)_q$ can be 'lifted' to an irreducible *-representation of $\mathbb{C}[SU_{2n}]_q$, this result is then used to show the existence of the universal enveloping $C^*$- algebra of $\mathrm{Pol}(\mathrm{Mat}_n)_q$ and to prove that it is isomorphic to the closure of the image of the Fock representation. Moreover, we also classify all irreducible $*$-representations of $\mathrm{Pol}(\mathrm{Mat}_n)_q$ using a diagram approach.

math.QA↗
arXiv2016

Half-centered Operators

An operator $T$ on a Hilbert space is called half-centered if the sequence $T^{*}T,(T^{*})^{2}T^{2},...$ consists of mutually commuting operators. It is a subclass of the well-studied centered operators. In this paper we give a condition for when a half-centered operator is centered and prove a structure theorem for those half-centered operators that satisfies a criteria of a technical nature.

math.FA↗