Journal of the Iranian Mathematical Society
https://jims.ims.ir/
Journal of the Iranian Mathematical Societyendaily1Sat, 01 Jan 2022 00:00:00 +0330Sat, 01 Jan 2022 00:00:00 +0330A generalization of Posner's theorem on generalized derivations in rings
https://jims.ims.ir/article_160787.html
&nbsp;In this paper, we generalize the Posner's theorem on generalized derivations in rings as follows: Let $\mathscr{A}$ be an arbitrary ring, $\mathscr{I}$ a non-zero ideal, $\mathscr{T}$ is a prime ideal of $\mathscr{A}$ such that $\mathscr{T}\subset \mathscr{I},$ and $\psi $ be a non-zero generalized derivation associated with a non-zero derivation $\rho $ of $\mathscr{A}.$ If one of the following conditions is satisfied: (i) $[\psi (x),x]\in \mathscr{T},$ (ii) $[[\psi (x),x],y]\in \mathscr{T},$ (iii) $\overline{[\psi (x),x]}\in \mathscr{Z}(\mathscr{A}/\mathscr{T})$ and (iv) $\overline{[[\psi (x),x],y]}\in \mathscr{Z}(\mathscr{A}/\mathscr{T})$ $\forall $ $x,y\in \mathscr{I},$ then $\rho (\mathscr{A})\subseteq \mathscr{T}$ or $\mathscr{A}/mathscr{T}$ is commutative. At the example, it is given that the hypothesis of the &nbsp;theorems are necessary.A tribute to Prof. O. A. S. Karamzadeh
https://jims.ims.ir/article_171361.html
&lrm;It gives me a great pleasure to write this short note about my meetings with prof&lrm;. &lrm;Karamzadeh&lrm;. &lrm;Of course his mathematical contribution will be mentioned by the experts&lrm;. &lrm;All dates given are according to the Iranian calendar&lrm;.Centralizer nearrings
https://jims.ims.ir/article_162441.html
Suppose that $(G,+)$ is a group (possibly nonabelian) and that $X$ is a submonoid of the monoid of all endomorphisms of $G$ under the operation of composition of functions, $({\rm End}~{G}, \circ)$. We define the $X$-centralizer nearring of $G$ by $X$ by saying that $M_X(G):=\{ f:G \to G \mid f(0_G)=0_G \text{ and } f \circ \alpha=\alpha \circ f \text{ for all } \alpha \in X \}$. This set of functions, $M_X(G)$, is a nearring under the ``usual" operations of function ``addition" and ``composition" of functions. This paper investigates how centralizer nearrings can be defined and investigates their ideals when $X$ is a group of automorphisms.Hochschild cohomology of Sullivan algebras and mapping spaces between manifolds
https://jims.ims.ir/article_169711.html
&lrm;Let $e&lrm;: &lrm;N^n \rightarrow M ^m$ be an embedding of closed&lrm;, &lrm;oriented manifolds of dimension $n$ and $m$ respectively&lrm;. &lrm;We study the relationship between the homology of the free loop space $LM$ on $M$ and of the space $L_NM$ of loops of $M$ based in $N$ and define a shriek map&lrm;&nbsp;&lrm;$ H_*(e)_{!}&lrm;: &lrm;H_*( LM&lrm;, &lrm;\mathbb{Q}) \rightarrow H_*( L_NM&lrm;, &lrm;\mathbb{Q})$ using Hochschild cohomology and study its properties&lrm;. &lrm;In particular we extend a result of F\'elix on the injectivity of the map induced by $ \aut_1M \rightarrow \map(N&lrm;, &lrm;M; f ) $ on rational homotopy groups when $M$ and $N$ have the same dimension and $ f&lrm;: &lrm;N\rightarrow M $ is a map of non zero degree&lrm;.Dichotomy between operators acting on finite and infinite dimensional Hilbert spaces
https://jims.ims.ir/article_171895.html
In this expository article, we give several examples showing how drastically different can be the behavior of operators acting on finite versus infinite dimensional Hilbert spaces. This essay is written as in such a friendly-reader to show that the situation in the infinite dimensional setting is trickier than the finite one.Asymptotically equicontinuous sequences of operators and a Banach--Steinhaus type theorem
https://jims.ims.ir/article_158793.html
We introduce the notion of an asymptotically equicontinuous sequence of linear operators, and use it to prove the following result. If $X,Y$ are topological vector spaces, if $T_n,T:X\to Y$ are continuous linear maps, and if $D$ is a dense subset of $X$, then the following statements are equivalent: $(i) ~T_nx\to Tx$ for all $x\in X$, and $(ii) ~T_n x\to Tx$ for all $x\in D$ and the sequence $(T_n)$ is asymptotically equicontinuous.Minimal generating sequences of F-subgroups
https://jims.ims.ir/article_163591.html
The behaviour of generating sets of finite groups has been widely studied, from several points of view. The purpose of this note is to investigate what happens when, instead of sets of elements generating a group, sets of subgroups belonging to a prescribed family are considered. Some known results on generating set can be extended and generalized, using similar arguments and techniques, but interesting open questions also arise.Bohr conditions and almost periodic means in quasi-complete spaces
https://jims.ims.ir/article_164823.html
We study Bohr conditions for functions on topological groups taking values in locally convex spaces. We show that functions satisfying Bohr conditions are uniformly continuous. We show that in quasi-complete spaces, Bohr conditions are equivalent to Bochner's characterizations of almost periodicity. We prove the existence of invariant mean for almost periodic functions with values in quasi-complete spaces.A topologist's interactions with Derek J. S. Robinson and his mathematics
https://jims.ims.ir/article_169710.html
The paper begins with a brief history of this topologist's interactions with Derek J. S. Robinson. It continues with a topological proof of Derek's result showing that the Schur multiplier of a generalized Baumslag-Solitar group $G$ is free abelian of rank one less than the rank of the torsion free first homology of $G$ and that both of these ranks can be computed by inspecting a weighted directed graph associate to $G$. In this paper the topology of a special subclass of Seifert fibred 2-dimensional complexes is used to provide proofs of Derek's results.Arens regularity of ideals in $A(G)$, $A_{cb}(G)$ and $A_M(G)$.
https://jims.ims.ir/article_171452.html
In 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.Order isomorphisms and order anti-isomorphisms on spaces of convex functions
https://jims.ims.ir/article_171766.html
For $i=1,2$, 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.Two classes of $J$-operators
https://jims.ims.ir/article_172063.html
We 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.