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Hoger Ghahramani

Publications and source records attributed to Hoger Ghahramani.

16 recordsLinked to original sources
arXiv2025

Characterization of Lie centralizable mappings on B(X)

Assume that B(X) is the algebra of all bounded linear operators on a complex Banach space X, and let W in B(X) is such that cl(W(X)) is not equal to X or W=zI, where z is a complex number and I is the identity operator. We show that if f: B(X) --> B(X) is an additive mapping Lie centralizable at W, then f(A)=kA+h(A) for all A in B(X), where k is a complex number and h:B(X)--> CI is an additive mapping such that h([A,B])=0 for all A,B in B(X) with AB=W.

math.FA↗
arXiv2024

Jordan and Lie derivations of $ϕ$-Johnson amenable Banach algebras

Let U be a $ϕ$-Johnson amenable Banach algebra in which $ϕ$ is a non-zero multiplicative linear functional on U. Suppose that X is a Banach U-bimodule such that $a.x=ϕ(a)x$ for all a in U and x in X or $x.a=ϕ(a)x$ for all a in U and x in X. We show that every continuous Jordan derivation from U to X is a derivation, and every continuous Lie derivation from U to X decomposed into the sum of a continuous derivation and a continuous center-valued trace.

math.FA↗
arXiv2024

Symmetrically pseudo-amenable Banach algebras

We introduce and study a new notion of amenability called symmetric pseudo-amenability. We obtain some properties of symmetrically pseudo-amenable Banach algebras and with examples, we compare this type of amenability with some other types of amenability. We also provide some special classes of symmetrically pseudo-amenable Banach algebras. Finally, Jordan and Lie derivations from a class of Banach algebras into appropriate Banach bimodules are investigated using the notion of symmetric pseudo-amenability.

math.FA↗
arXiv2020

Ternary derivations of nest algebras

Suppose that $X$ is a (real or complex) Banach space, $dimX \geq 2$, and $\mathcal{N}$ is a nest on $X$, with each $N$ in $\mathcal{N}$ is complemented in $X$ whenever $N_{-}=N$. A ternary derivation of $Alg\mathcal{N}$ is a triple of linear maps $(γ, δ, τ)$ of $Alg\mathcal{N}$ such that $γ(AB)=δ(A)B +Aτ(B)$ for all $A,B \in Alg\mathcal{N}$. We show that for linear maps $δ$, $τ$ on $Alg\mathcal{N}$ there exists a unique linear map $γ$ from $Alg\mathcal{N}$ into $Alg\mathcal{N}$ defined by $γ(A)=RA+AT$ for some $R$, $T$ in $Alg\mathcal{N}$ such that $(γ, δ, τ)$ is a ternary derivation of $Alg\mathcal{N}$ if and only if $δ$, $τ$ satisfy $δ(A)B+Aτ(B)=0$ for any $A$,$B$ in $Alg\mathcal{N}$ with $AB=0$. We also prove that every ternary derivation on $Alg\mathcal{N}$ is an inner ternary derivation. Our results are applied to characterize the (right or left) centralizers and derivations through zero products, local right (left) centralizers, right (left) ideal preserving maps and local derivations on nest algebras.

math.OA↗
arXiv2019

Relative amenability of Banach algebras

Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of triangular Banach algebras and Banach algebras associated to locally compact groups. We generalize some of the previous known results by applying the concept of relative amenability of Banach algebras, especially, we present a generalization of Johnson's theorem in the concept of relative amenability.

math.FA↗
arXiv2019

Automatic continuity of Some linear mappings from certain products of Banach algebras

Let $\mathcal{A}$ and $\mathcal{U}$ be Banach algebras and $θ$ be a nonzero character on $\mathcal{A}$. Then the \textit{Lau product Banach algebra} $\mathcal{A}\times_θ\mathcal{U}$ associated with the Banach algebras $\mathcal{A}$ and $\mathcal{U}$ is the $l^1$-direct sum $\mathcal{A}\oplus\mathcal{U}$ equipped with the algebra multiplication $(a,u)(a',u')=(ab,θ(a)u'+θ(a')u+uu')\, (a,a'\in\mathcal{A},u,u'\in\mathcal{U})$ and $l^1$-norm. In this paper we shall investigate the derivations and multipliers from this Banach algebras and study the automatic continuity of these mappings. We also study continuity of the derivations for some special cases of Banach algebra $\mathcal{U}$ and Banach $\mathcal{A}\times_θ\mathcal{U}$-bimodule $\mathcal{X}$ and establish various results on the continuity of derivations and give some examples.

math.FA↗
arXiv2018

Left Ideal Preserving Maps on Triangular Algebras

Let A be a unital algebra over a commutative unital ring R. We say that A is a SLIP algebra if every R-linear map on A that leaves invariant every left ideal of A is a left multiplier. In this paper we study whether a triangular algebra Tri(A,M,B) is a SLIP algebra and give some necessary or sufficient conditions for a triangular algebra be a SLIP algebra, and various examples are given which illustrate limitations on extending some of the theory developed. Then our results are applied to generalized triangular matrix algebras and block upper triangular algebras. Also, some SLIP algebras other that triangular algebras are provided.

math.RA↗
arXiv2016

Derivations on semidirect products of Banach algebras

Let A and U be Banach algebras such that U is also a Banach A- bimodule with compatible algebra operations, module actions and norm. By defining an approprite action, we turn l1-direct product A item U into a Banach algebra such that A is closed subalgebra and U is a closed ideal of it. This algebra, is in fact semidirect product of A and U which we denote it by A litem U and every semidirect products of Banach algebras can be represented as this form. In this paper we consider the Banach algebra A litem U as mentioned and study the derivations on it. In fact we consider the automatic continuity of the derivations on A litem U and obtain some results in this context and study its relation with the automatic continuity of the derivations on A and U. Also we calculate the first cohomology group of A litem U in some different cases and establish relations among the first cohomology group of A litem U and those of A and U. As applications of these contents, we present various results about the automatic continuity of derivations and the first cohomology group of direct products of Banach algebras, module extension Banach algebras and theta Lau products of Banach algebras.

math.FA↗
arXiv2014

2n-Weak module amenability of semigroup algebras

Let $S$ be an inverse semigroup with the set of idempotents $E$. We prove that the semigroup algebra $\ell^{1}(S)$ is always $2n$-weakly module amenable as an $\ell^{1}(E)$-module, for any $n\in \mathbb{N}$, where $E$ acts on $S$ trivially from the left and by multiplication from the right.

math.FA↗
arXiv2014

Jordan derivations on block upper triangular matrix algebras

We provide that any Jordan derivation from the block upper triangular matrix algebra $\T = \T(n_{1},n_{2}, \cdots, n_{k})\subseteq M_{n}(\mathbb{\C})$ into a $2$-torsion free unital $\T$-bimodule is the sum of a derivation and an antiderivation.

math.RA↗
arXiv2014

On derivations and Jordan derivations through zero products

Let $\A$ be a unital complex (Banach) algebra and $\M$ be a unital (Banach) $\A$-bimodule. The main results describe (continuous) derivations or Jordan derivations $D:\A\rightarrow \M$ through the action on zero products, under certain conditions on $\A$ and $\M$. The proof is based on the consideration of a (continuous) bilinear map satisfying a related condition.

math.RA↗
arXiv2014

Characterizing Jordan centralizers and Jordan generalized derivations on triangular rings through zero products

Let $\T$ be a $2$-torsion free triangular ring and let $φ:\T\rightarrow \T$ be an additive map. We prove that if $\A φ(\B)+φ(\B)\A=0$ whenever $\A,\B\in \T$ are such that $\A\B=\B\A=0$, then $φ$ is a centralizer. It is also shown that if $τ:\T\rightarrow \T$ is an additive map satisfying $\label{t2} X,Y\in \T, \quad XY=YX=0\Rightarrow X τ(Y)+δ(X)Y+Yδ(X)+τ(Y)X=0$, where $δ:\T\rightarrow \T $ is an additive map satisfies $X,Y\in \T, \quad XY=YX=0\Rightarrow X δ(Y)+δ(X)Y+Yδ(X)+δ(Y)X=0$, then $τ(\A)=d(\A)+\A τ(\textbf{1})$, where $d:\T\rightarrow \T$ is a derivation and $τ(\textbf{1})$ lies in the centre of the $\T$. By applying this results we obtain some corollaries concerning (Jordan) centralizers and (Jordan) derivations on triangular rings.

math.RA↗
arXiv2014

Characterizations of left derivable maps at non-trivial idempotents on nest algebras

Let $Alg \mathcal{N}$ be a nest algebra associated with the nest $ \mathcal{N}$ on a (real or complex) Banach space $\X$. Suppose that there exists a non-trivial idempotent $P\in Alg\mathcal{N}$ with range $P(\X) \in \mathcal{N}$ and $δ:Alg\mathcal{N} \rightarrow Alg\mathcal{N}$ is a continuous linear mapping (generalized) left derivable at $P$, i.e. $δ(ab)=aδ(b)+bδ(a)$ ($δ(ab)=aδ(b)+bδ(a)-baδ(I)$) for any $a,b\in Alg\mathcal{N}$ with $ab=P$. we show that $δ$ is a (generalized) Jordan left derivation. Moreover, we characterize the strongly operator topology continuous linear maps $δ$ on some nest algebra $Alg\mathcal{N}$ with property that $δ(P)=2Pδ(P)$ or $δ(P)=2Pδ(P)-Pδ(I)$ every idempotent $P$ in $Alg\mathcal{N}$.

math.OA↗
arXiv2013

Characterizing Jordan derivations of matrix rings through zero products

Let $\Mn$ be the ring of all $n \times n$ matrices over a unital ring $\mathcal{R}$, let $\mathcal{M}$ be a 2-torsion free unital $\Mn$-bimodule and let $D:\Mn\rightarrow \mathcal{M}$ be an additive map. We prove that if $D(\A)\B+ \A D(\B)+D(\B)\A+ \B D(\A)=0$ whenever $\A,\B\in \Mn$ are such that $\A\B=\B\A=0$, then $D(\A)=δ(\A)+\A D(\textbf{1})$, where $δ:\Mn\rightarrow \mathcal{M}$ is a derivation and $D(\textbf{1})$ lies in the centre of $\mathcal{M}$. It is also shown that $D$ is a generalized derivation if and only if $D(\A)\B+ \A D(\B)+D(\B)\A+ \B D(\A)-\A D(\textbf{1})\B-\B D(\textbf{1})\A=0$ whenever $\A\B=\B\A=0$. We apply this results to provide that any (generalized) Jordan derivation from $\Mn$ into a 2-torsion free $\Mn$-bimodule (not necessarily unital) is a (generalized) derivation. Also, we show that if $φ:\Mn\rightarrow \Mn$ is an additive map satisfying $φ(\A \B+\B \A)=\Aφ(\B)+φ(\B)\A \quad (\A,\B \in \Mn)$, then $φ(\A)=\Aφ(\textbf{1})$ for all $\A\in \Mn$, where $φ(\textbf{1})$ lies in the centre of $\Mn$. By applying this result we obtain that every Jordan derivation of the trivial extension of $\Mn$ by $\Mn$ is a derivation.

math.RA↗