Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124120230101A tribute to Prof. O. A. S. Karamzadeh1417136110.30504/jims.2023.394235.1107ENM. R.DarafshehSchool of mathematics, statistics and computer science, College of science, University of Tehran, Tehran, Iran.0000-0002-5539-4989Journal Article20230422It gives me a great pleasure to write this short note about my meetings with prof. Karamzadeh. Of course his mathematical contribution will be mentioned by the experts. All dates given are according to the Iranian calendar.https://jims.ims.ir/article_171361_fec2797052ff5da9f0974784ce1ba8f8.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124120230101Arens regularity of ideals in $A(G)$, $A_{cb}(G)$ and $A_M(G)$.52517145210.30504/jims.2023.385500.1091ENB.ForrestDepartment of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.J.SawatzkyDepartment of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.A.ThamizhazhaganDepartment of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.Journal Article20230213In this paper, we look at the question of when various ideals in the Fourier algebra $A(G)$ or its closures $A_M(G)$ and $A_{cb}(G)$ in, respectively, its multiplier and $cb$-multiplier algebra are Arens regular. We show that in each case, if a non-zero ideal is Arens regular, then the underlying group $G$ must be discrete. In addition, we show that if an ideal $I$ in $A(G)$ has a bounded approximate identity, then it is Arens regular if and only if it is finite-dimensional.https://jims.ims.ir/article_171452_757f30a2988d0c0f2d7430947e4be2f2.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124120230101Order isomorphisms and order anti-isomorphisms on spaces of convex functions274417176610.30504/jims.2023.385243.1089END. H.LeungDepartment of Mathematics, National University of Singapore, Singapore, Republic of Singapore.Journal Article20230209For $i=1,2$, let $C_i$ be a convex set in a locally convex Hausdorff topological vector space $X_i$. Denote by $\operatorname{conv}(C_i)$ the space of all convex, proper, lower semicontinuous functions on $C_i$. A representation is given of any bijection $T:\operatorname{conv}(C_1)\to \operatorname{conv}(C_2)$ that preserves the pointwise order. For $X_i = \mathbb{R}^n$, this recovers a result of Artstein-Avidan and Milman and its generalization by Cheng and Luo. If $X_1$ is a Banach space and $X_2 = X^*_1$ with the weak$^*$-topology, it gives a result due to Iusem, Reem and Svaiter. We also obtain representation of order reversing bijections and thus a characterization of the Legendre transform, generalizing the same result by Artstein-Avidan and Milman for the $\mathbb{R}^n$ case. The result on order isomorphisms actually holds for convex functions with values in ordered topological vector spaces.https://jims.ims.ir/article_171766_00f3ebc069f28c08d1210e963637654e.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124120230101Two classes of $J$-operators455417206310.30504/jims.2023.395366.1111ENT.AndoHokkaido University (Emeritus), Sapporo, JapanJournal Article20230501We define two classes ${\mathfrak A}$ and ${\mathfrak B}$ in the space ${\mathcal B}({\mathcal H})$ of operators acting on a Hilbert space on the basis of $J$-order relation and spectra, and discuss various properties related to these classes.https://jims.ims.ir/article_172063_2b2cf48e99317f5a99faf40d60f4f383.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124120230101On the mutipliers of the Figá-Talamanca Herz algebra556617221510.30504/jims.2023.365376.1076ENA.DerighettiMA A1 345 (B^atiment MA) Station 8 CH-1015 Lausanne.Journal Article20221011Let $G$ be a locally compact group and $p,q \in \mathbb{R}$ with $p>1, \hskip2pt p\not =2$ and $q$ between $2$ and $p$ (if $p<2$ then $p<q<2,$ if $p>2$ then $2<q<p$.) The main result of the paper is that $ A_{q}(G)$ multiplies $A_p(G),$ more precisely we show that the Banach algebra $A_p(G)$ is a Banach module on $A_q(G).$https://jims.ims.ir/article_172215_be98bddd8bbd2dfa29719595275cd720.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16124120230101Commutators and hyponormal operators on a Hilbert space677817236710.30504/jims.2023.393155.1106ENM.AkhmadievKazan National Research Technological University, Kazan, RussiaH.AlhasanDepartment of Mathematics and Mechanics, Kazan Federal University, Kazan, RussiaA.BikchentaevDepartment of Mathematics and Mechanics, Kazan Federal University, Kazan, RussiaP.IvanshinDepartment of Mathematics and Mechanics, Kazan Federal University, Kazan, RussiaJournal Article20230414Let $\mathcal{H}$ be an infinite-dimensional Hilbert space over the field $\mathbb{C}$, $\mathcal{B}(\mathcal{H})$ be the $\ast$-algebra of all linear bounded operators on $\mathcal{H}$, let $|X|=\sqrt{X^*X}$ for $X\in \mathcal{B}(\mathcal{H})$. An operator $A\in \mathcal{B}(\mathcal{H})$ is a commutator if $A=[S, T]=ST-TS$ for some $S, T\in \mathcal{B}(\mathcal{H})$. Let $X, Y \in \mathcal{B}(\mathcal{H})$ and $X\geq 0$. If the operator $XY$ is a non-commutator, then $X^pYX^{1-p}$ is a non-commutator for every $0<p<1$. Let $A \in \mathcal{B}(\mathcal{H})$ be $p$-hyponormal for some $0<p\leq 1$. If $|A^*|^r$ is a non-commutator for some $r>0$ then $|A|^q$ is a non-commutator <br />for every $q>0$. Let $\mathcal{H}$ be separable and $A \in \mathcal{B}(\mathcal{H})$ be a non-commutator. If $A$ is hyponormal (or cohyponormal) then $A$ is normal. We also present results in the case of a finite-dimensional Hilbert space.https://jims.ims.ir/article_172367_fa70bbc47cad13970c496623023f2552.pdf