scholarly journals Characterization of mixed n-Jordan and pseudo n-Jordan homomorphisms

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1989-2002
Author(s):  
Masoumeh Neghabi ◽  
Abasalt Bodaghi ◽  
Abbas Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Jordan Homomorphism ◽  
Mild Conditions ◽  
Jordan Homomorphisms ◽  
Semisimple Banach Algebra

In this article, a new notion of n-Jordan homomorphism namely the mixed n-Jordan homomorphism is introduced. It is proved that how a mixed (n + 1)-Jordan homomorphism can be a mixed n-Jordan homomorphism and vice versa. By means of some examples, it is shown that the mixed n-Jordan homomorphisms are different from the n-Jordan homomorphisms and the pseudo n-Jordan homomorphisms. As a consequence, it shown that every mixed Jordan homomorphism from Banach algebra A into commutative semisimple Banach algebra B is automatically continuous. Under some mild conditions, every unital pseudo 3-Jordan homomorphism is a homomorphism.

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

2018 ◽  
Vol 11 (02) ◽  
pp. 1850021 ◽  
Author(s):  
A. Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Unital Banach Algebra

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

scholarly journals A Characterization of Bi-Jordan Homomorphisms on Banach Algebras

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Abbas Zivari-Kazempour
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms

For Banach algebras A and B, we show that if U=A×B is unital and commutative, each bi-Jordan homomorphism from U into a semisimple commutative Banach algebra D is a bihomomorphism.

scholarly journals Characterization of $n$-Jordan Homomorphisms on Rings

2021 ◽  
Vol 53 ◽  
Author(s):  
Abbas Zivari-kazempour ◽  
Mohammad Valaei
Keyword(s):  
Jordan Homomorphism ◽  
Jordan Homomorphisms

In this paper, we prove that if $\varphi:\mathcal{R}\longrightarrow\mathcal{R}'$ is an $n$-Jordan homomorphism, where $\mathcal{R}$ has a unit $e$, then the map $a\longmapsto \varphi(e)^{n-2}\varphi(a)$ is a Jordan homomorphism.  As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.

scholarly journals Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yang-Hi Lee
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Ring Homomorphism ◽  
Normed Algebra ◽  
Jordan Homomorphism ◽  
Commutative Banach Algebras ◽  
Jordan Homomorphisms

We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.

Amalgamated duplication of the Banach algebra 𝔄 along a 𝔄-bimodule 𝒜

2018 ◽  
Vol 17 (09) ◽  
pp. 1850169 ◽  
Author(s):  
Hossein Javanshiri ◽  
Mehdi Nemati
Keyword(s):  
Banach Algebra ◽  
Cohomology Group ◽  
Banach Algebras ◽  
Multiplier Algebra ◽  
Topological Center ◽  
Maximal Ideals ◽  
Open Questions ◽  
Arens Regularity ◽  
Amalgamated Duplication

Let [Formula: see text] and [Formula: see text] be Banach algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with compatible actions. We define the product [Formula: see text], which is a strongly splitting Banach algebra extension of [Formula: see text] by [Formula: see text]. After characterization of the multiplier algebra, topological center, (maximal) ideals and spectrum of [Formula: see text], we restrict our investigation to the study of semisimplicity, regularity, Arens regularity of [Formula: see text] in relation to that of the algebras [Formula: see text], [Formula: see text] and the action of [Formula: see text] on [Formula: see text]. We also compute the first cohomology group [Formula: see text] for all [Formula: see text] as well as the first-order cyclic cohomology group [Formula: see text], where [Formula: see text] is the [Formula: see text]th dual space of [Formula: see text] when [Formula: see text] and [Formula: see text] itself when [Formula: see text]. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for Lau products and module extensions of Banach algebras as well as triangular Banach algebra. Finally, special attention is devoted to the cyclic and [Formula: see text]-weak amenability of [Formula: see text]. In this context, several open questions arise.

scholarly journals H/D Exchange Under Mild Conditions in Arenes and Unactivated Alkanes with C6D6 and D2O Using Rigid, Electron-rich Iridium PCP Pincer Complexes

2020 ◽  
Author(s):  
Joel D. Smith ◽  
George Durrant ◽  
Daniel Ess ◽  
Warren Piers
Keyword(s):  
Hydrogen Isotope ◽  
Isotope Exchange ◽  
Room Temperature ◽  
Pincer Complexes ◽  
Synthesis And Characterization ◽  
Hydrogen Isotope Exchange ◽  
Mild Conditions ◽  
Highly Active ◽  
Pcp Pincer

<div>The synthesis and characterization of an iridium polyhydride complex (Ir-H4)</div><div>supported by an electron-rich PCP framework is described. This complex readily loses molecular</div><div>hydrogen allowing for rapid room temperature hydrogen isotope exchange (HIE) at the hydridic</div><div>positions and the α-C-H site of the ligand with deuterated solvents such as benzene-d6, toluene-d8</div><div>and THF-d8. The removal of 1-2 equivalents of molecular H2 forms unsaturated iridium carbene</div><div>trihydride (Ir-H3) or monohydride (Ir-H) compounds that are able to create further unsaturation</div><div>by reversibly transferring a hydride to the ligand carbene carbon. These species are highly active</div><div>hydrogen isotope exchange (HIE) catalysts using C6D6 or D2O as deuterium sources for the</div><div>deuteration of a variety of substrates. By modifying conditions to influence the Ir-Hn speciation,</div><div>deuteration levels can range from near exhaustive to selective only for sterically accessible sites.</div><div>Preparative level deuterations of select substrates were performed allowing for procurement of</div><div>>95% deuterated compounds in excellent isolated yields; the catalyst can be regenerated by</div><div>treatment of residues with H2 and is still active for further reactions.</div>

scholarly journals On Fully Stable Banach Algebra Modules and Fully Pesudo Stable Banach Algebra Modules

2018 ◽  
Vol 15 (1) ◽  
pp. 102-105 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Banach Algebra ◽  
Algebra Module

The concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.

Efficient pseudo five-component synthesis of 4,4′-(arylmethylene)-bis(3-methyl-1-phenyl-1H-pyrazol-5-ol) derivatives promoted by a novel ionic liquid catalyst

2018 ◽  
Vol 73 (3-4) ◽  
pp. 191-195 ◽  
Author(s):  
Zahra Abshirini ◽  
Abdolkarim Zare
Keyword(s):  
Ionic Liquid ◽  
Disulfonic Acid ◽  
Thermal Gravimetric ◽  
One Pot ◽  
Mild Conditions ◽  
Acidic Ionic Liquid ◽  
Brønsted Acidic Ionic Liquid ◽  
The One ◽  
C Nmr

AbstractIn this research, initial production and characterization of a novel Brønsted-acidic ionic liquid, namely,N,N,N′,N′-tetramethylethylenediaminium-N,N′-disulfonic acid hydrogen sulfate ([TMEDSA][HSO4]2), has been described (characterization was achieved using Fourier-transform infrared spectroscopy,1H nuclear magnetic resonance (NMR),13C NMR, and mass and thermal gravimetric spectra). Thereafter, utilization of [TMEDSA][HSO4]2as a highly effectual catalyst for the synthesis of 4,4′-(arylmethylene)-bis(3-methyl-1-phenyl-1H-pyrazol-5-ol) derivatives through the one-pot pseudo five-component reaction of phenylhydrazine (2 eq.) with ethyl acetoacetate (2 eq.) and arylaldehydes (1 eq.) in relatively mild conditions, has been reported.

scholarly journals φ-Multipliers on Banach Algebras and Topological Modules

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Marjan Adib
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Topological Module ◽  
Topological Modules ◽  
Arens Regularity

We prove some results concerning Arens regularity and amenability of the Banach algebraMφAof allφ-multipliers on a given Banach algebraA. We also considerφ-multipliers in the general topological module setting and investigate some of their properties. We discuss theφ-strict andφ-uniform topologies onMφA. A characterization ofφ-multipliers onL1G-moduleLpG, whereGis a compact group, is given.

Sign in / Sign up

Export Citation Format

Share Document