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Mahmood Alaghmandan

Publications and source records attributed to Mahmood Alaghmandan.

At least 19 recordsLinked to original sources
arXiv2026

What Quantitative Risk Modellers Can Learn from Durkheim's Study of Suicide

Emile Durkheim's Suicide: A Study in Sociology (1897) predates much of the statistical machinery that quantitative modellers now take for granted. Yet, working with sparse and imperfect observational data, Durkheim repeatedly arrives at practices that remain remarkably relevant to modern modelling. This paper revisits Suicide from the perspective of quantitative risk modelling, not for its substantive conclusions, but for the reasoning by which Durkheim reached them. His approach illustrates how careful definition, common sense, logical investigation, scepticism toward convenient explanations, and close attention to what the data can and cannot support---all of which must precede, and can often substitute for, statistical sophistication. The broader lesson is simple: good modelling begins not with technique, but with understanding the problem, interrogating the evidence, and reasoning carefully about what it can actually tell us.

q-fin.RM↗
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↗
arXiv2026

A Methodology to Measure Impacts of Scenarios Through Expected Credit Losses

In this paper, we present a methodology for measuring the impact of scenarios on the expected losses of exposures by leveraging the existing provisioning infrastructure within financial institutions, where scenario effects are captured through changes in probabilities of default. We then describe how to design and implement a scenario test where risk drivers are given for standardized groupings of exposures, and the groupings are defined based on common features of the exposures. The methodology presented served as a theoretical foundation for the standardized climate scenario exercise conducted in 2024 by the Office of the Superintendent of Financial Institutions of Canada and Quebec's Autorite des Marches Financiers.

q-fin.RM↗
arXiv2018

Remarks on weak amenability of hypergroups

We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the Cowling-Haagerup constant 1. As a corollary, we answer an open question of Eymard on Jacobi hypergroups. We also characterize the existence of bounded approximate identities for the hypergroup Fourier algebras of ultraspherical hypergroups.

math.FA↗
arXiv2018

A new duality via the Haagerup tensor product

We initiate the study of a new notion of duality defined with respect to the module Haagerup tensor product. This notion not only recovers the standard operator space dual for Hilbert $C^*$-modules, it also captures quantum group duality in a fundamental way. We compute the so-called Haagerup dual for various operator algebras arising from $\ell^p$ spaces. In particular, we show that the dual of $\ell^1$ under any operator space structure is $\min\ell^\infty$. In the setting of abstract harmonic analysis we generalize a result of Varopolous by showing that $C(\mathbb{G})$ is an operator algebra under convolution for any compact Kac algebra $\mathbb{G}$. We then prove that the corresponding Haagerup dual $C(\mathbb{G})^h=\ell^\infty(\widehat{\mathbb{G}})$, whenever $\widehat{\mathbb{G}}$ is weakly amenable. Our techniques comprise a mixture of quantum group theory and the geometry of operator space tensor products.

math.OA↗
arXiv2018

Mapping ideals of quantum group multipliers

We study the dual relationship between quantum group convolution maps $L^1(\mathbb{G})\rightarrow L^{\infty}(\mathbb{G})$ and completely bounded multipliers of $\widehat{\mathbb{G}}$. For a large class of locally compact quantum groups $\mathbb{G}$ we completely isomorphically identify the mapping ideal of row Hilbert space factorizable convolution maps with $M_{cb}(L^1(\widehat{\mathbb{G}}))$, yielding a quantum Gilbert representation for completely bounded multipliers. We also identify the mapping ideals of completely integral and completely nuclear convolution maps, the latter case coinciding with $\ell^1(\widehat{b\mathbb{G}})$, where $b\mathbb{G}$ is the quantum Bohr compactification of $\mathbb{G}$. For quantum groups whose dual has bounded degree, we show that the completely compact convolution maps coincide with $C(b\mathbb{G})$. Our techniques comprise a mixture of operator space theory and abstract harmonic analysis, including Fubini tensor products, the non-commutative Grothendieck inequality, quantum Eberlein compactifications, and a suitable notion of quasi-SIN quantum group, which we introduce and exhibit examples from the bicrossed product construction. Our main results are new even in the setting of group von Neumann algebras $VN(G)$ for quasi-SIN locally compact groups $G$.

math.OA↗
arXiv2016

Fourier algebras of hypergroups and central algebras on compact (quantum) groups

This paper concerns the study of regular Fourier hypergroups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizations of group amenability, introduce a notion of weak amenability for hypergroups, and show that every discrete commutative hypergroup is weakly amenable with constant 1. Using similar techniques, we provide a sufficient condition for amenability of hypergroup Fourier algebras, which, as an immediate application, answers one direction of a conjecture of Azimifard--Samei--Spronk [J. Funct. Anal. 256(5) 1544-1564, 2009] on the amenability of $ZL^1(G)$ for compact groups $G$. In the final section we consider Fourier algebras of hypergroups arising from compact quantum groups $\mathbb{G}$, and in particular, establish a completely isometric isomorphism with the center of the quantum group algebra for compact $\mathbb{G}$ of Kac type.

math.FA↗
arXiv2016

Dual space and hyperdimension of compact hypergroups

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.

math.RT↗
arXiv2016

Character density in central subalgebras of compact quantum groups

We investigate quantum group generalizations of various density results from Fourier analysis on compact groups. In particular, we establish the density of characters in the space of fixed points of the conjugation action on $L^2(\mathbb{G})$, and use this result to show the weak* density of characters in $ZL^{\infty}(\mathbb{G})$. At the level of $L^1(\mathbb{G})$, we show that the center $\mathcal{Z}(L^1(\mathbb{G}))$ is precisely the closed linear span of the quantum characters for a large class of compact quantum groups, including arbitrary compact Kac algebras. In the latter setting, we show, in addition, that $\mathcal{Z}(L^1(\mathbb{G}))$ is a completely complemented $\mathcal{Z}(L^1(\mathbb{G}))$-submodule of $L^1(\mathbb{G})$.

math.OA↗
arXiv2016

Amenability notions of hypergroups and some applications to locally compact groups

Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study the Leptin condition for discrete hypergroups derived from the representation theory of some classes of compact groups. Studying amenability of the hypergroup algebras for discrete commutative hypergroups, we obtain some results on amenability properties of some central Banach algebras on compact and discrete groups.

math.FA↗
arXiv2016

Weighted discrete hypergroups

Weighted group algebras have been studied extensively in Abstract Harmonic Analysis where complete characterizations have been found for some important properties of weighted group algebras, namely amenability and Arens regularity. One of the generalizations of weighted group algebras is weighted hypergroup algebras. Defining weighted hypergroups, analogous to weighted groups, we study Arens regularity and isomorphism to operator algebras for them. We also examine our results on three classes of discrete weighted hypergroups constructed by conjugacy classes of FC groups, the dual space of compact groups, and hypergroup structure defined by orthogonal polynomials. We observe some unexpected examples regarding Arens regularity and operator isomorphisms of weighted hypergroup algebras.

math.FA↗
arXiv2015

Seminormed $\ast$-subalgebras of $\ell^{\infty}(X)$

Arbitrary representations of a commutative unital ($\ast$-) $\mathbb{F}$-algebra $A$ as a subalgeba of $\mathbb{F}^X$ are considered, where $\mathbb{F}=\mathbb{C}$ or $\mathbb{R}$ and $X\neq\emptyset$. The Gelfand spectrum of $A$ is explained as a topological extension of $X$ where a seminorm on the image of $A$ in $\mathbb{F}^X$ is present. It is shown that among all seminormes, the $\sup$-norm is of special importance which reduces $\mathbb{F}^X$ to $\ell^{\infty}(X)$. The Banach subalgebra of $\ell^{\infty}(X)$ of all $Σ$-measurable bounded functions on $X$, is studied for which $Σ$ is a $σ$-algebra of subsets of $X$. In particular, we study lifting of positive measures from $(X, Σ)$ to the Gelfand spectrum of this algebra and observe an unexpected shift in the support of measures. In the case that $Σ$ is the Borel algebra of a topology, we study the relation of the underlying topology of $X$ and the one of the Gelfand spectrum.

math.FA↗
arXiv2015

Projections in $L^1(G)$; the unimodular case

We consider the issue of describing all self-adjoint idempotents (projections) in $L^1(G)$ 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 $L^1(G)$ 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 $L^1(G)$ for $G$ belonging to a class of groups that includes $SL(2,R)$ and all almost connected nilpotent locally compact groups.

math.RT↗
arXiv2015

Amenability properties of the central Fourier algebra of a compact group

We let the central Fourier algebra, ZA(G), be the subalgebra of functions u in the Fourier algebra A(G) of a compact group, for which u(xyx^{-1})=u(y) for all x,y in G. We show that this algebra admits bounded point derivations whenever G contains a non-abelian closed connected subgroup. Conversely when G is virtually abelian, then ZA(G) is amenable. Furthermore, for virtually abelian G, we establish which closed ideals admit bounded approximate identities. We also show that if ZA(G) is weakly amenable, even hyper-Tauberian, exactly when G admits no non-abelian connected subgroup. We also study the amenability constant of ZA(G) for finite G and exhibit totally disconnected groups G for which ZA(G) is non-amenable.

math.FA↗
arXiv2013

Separating maps between commutative Banach algebras

Let $\cal A$ and $\cal B$ be Banach algebras. A linear map $T:{\cal A} \rightarrow {\cal B}$ is called separating or disjointness preserving if $ab=0$ implies $Ta\;Tb = 0$ for all $a,b\in {\cal A}$. In this paper, we study a new class of regular Tauberian algebras and prove that some well-known Banach algebras in harmonic analysis belong to this class. We show that a bijective separating map between these algebras turns out to be continuous and the maximal ideal spaces of underlying algebras are homeomorphic. By imposing extra conditions on these algebras, we find a more thorough characterization of separating maps. The existence of a bijective separating map also leads to the existence of an algebraic isomorphism in some cases.

math.FA↗
arXiv2013

ZL-amenability and characters for the restricted direct products of finite groups

Let $G$ be a restricted direct product of finite groups $\{G_i \}_{i\in I}$, and let $\Zl^1(G)$ denote the centre of its group algebra. We show that $\Zl^1(G)$ is amenable if and only if $G_i$ is abelian for all but finitely many $i$, and characterize the maximal ideals of $\Zl^1(G)$ which have bounded approximate identities. We also study when an algebra character of $\Zl^1(G)$ belongs to $c_0$ or $\ell^p$ and provide a variety of examples.

math.FA↗