Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.     

Characterizations of ( m,n )-Jordan Derivations and ( m,n )-Jordan Derivable Mappings on Some Algebras

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A~2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.     

Group inverse and core inverse in Banach and C*-algebras

Abstract

In this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14].     

直觉I-Fuzzy拓扑空间的杨忠道定理

以L~*-格值上Lukasiewicz蕴含算子为工具引入了直觉I-Fuzzy拓扑空间中导集概念,接着给出它的一些性质,最后证明了直觉I-Fuzzy拓扑空间中导集的杨忠道定理.     

一类特定的AF-代数

讨论了一类特定的AF-代数,其上的恒等同态可以用一列有限维值域的自同态逐点逼近.给出了这类AF-代数的K-理论刻画,并给出了一个不在这一类中的RFD AF-代数的例子.     

The study of phase,microstructure, and magnetocaloric properties in LaFe11.6*xSi1.4B0.1 alloys

The effect of Fe on the phase and magnetocaloric property of LaFe_11.6*xSi_1.4B_0.1 alloys with x = 1.0–1.4 have been studied. The results show that the excess of Fe will make the α-Fe phases increase, but the easy corrosion LaFeSi phase reduces in LaFe_11.6*xSi_1.4B_0.1 alloys. All LaFe_11.6*xSi_1.4B_0.1 alloys keep the first-order magnetic phase transition. The saturation magnetizations of LaFe_11.6*xSi_1.4B_0.1 alloys with x > 1 are much higher than LaFe_11.6Si_1.4B_0.1 alloy under 2T magnetic field. This results in the maximum isothermal magnetic entropy changes, and the relative cooling power of LaFe_11.6*xSi_1.4B_0.1 alloys is bigger than for LaFe_11.6Si_1.4B_0.1 alloys.     

Photoinduced phase transitions and helix untwisting in the SmC* phase of a novel cinnamoyl-based liquid crystal

A photoinduced phase transition and helix untwisting in a new liquid crystal forming the SmC* phase were studied in detail. The compound consists of a cinnamoyl photosensitive fragment with C?=?C double bond capable of photoisomerisation and photocycloaddition. It was shown that ultraviolet (UV) irradiation (365 nm) induces an extreme decrease in phase transitions temperatures (SmC*–SmA*, SmA*–N*, N*–I). Vertically aligned samples in the SmC* phase cause selective light reflection in the visible spectral range. The light action results in a noticeable helix untwisting that causes a shift in the selective light reflection peak to the long-wavelength spectral region. The temperature dependence of spontaneous polarisation P _s was measured and it was found that UV irradiation induces a decrease in the values of P _s. Photo-optical phenomena taking place in the liquid crystal are attributed to the formation of photoproducts having low anisometry, which disrupts mesophases.     

Universal C*-algebras defined by completely bounded unital homomorphisms

Suppose A is a unital C*-algebra and r 1.In this paper,we define a unital C*-algebra C_(cb)*(A,r) and a completely bounded unital homomorphism α_r:A → C_(cb)*(A,r)with the property that C_(cb)*(A,r)=C*(α_r(A))and,for every unital C*-algebra B and every unital completely bounded homomorphism φ:A→ B,there is a(unique)unital *-homomorphism π:C_(cb)*(A,r)→B such thatφ=πoα_r.We prove that,if A is generated by a normal set {t_λ:λ∈Λ},then C_(cb)*(A,r)is generated by the set {α_r(t_λ):λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C_(cb)*(A,r)we obtain that,if Β is a unital C*-algebra that can be embedded into A,then C_(cb)*(B,r)can be naturally embedded into C(cb)*(A,r).We give characterizations of C_(cb)*(A,r)for some special situations and we conclude that C_(cb)*(A,r)will be "nice" when dim(A)≤ 2 and "quite complicated" when dim(A)≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C_(cb)*(A,r).We also define and study some analogous of C_(cb)*(A,r).     

Synthesis,spatial structure and spectral properties of pyrylo‐4 (thio) squaraines variously substituted in cyclobutene moiety

Synthetic routes have been developed to a number of (thio) squaraine dyes containing the residues of CH‐acids at the central cyclobutene ring. The electronic and spatial structure as well as the chemical conversions and optical behaviour of the compounds obtained have been studied both theoretically and by X‐ray diffraction analysis, ¹H NMR and electronic spectroscopy. As shown, the electronic nature and sterical characteristics of the central ring substituents give rise to some general conformational features and crystal packing regularities and also govern the spectral position of the first π–π^* absorption band. The structure–property relationships established in the study provide guidance for the purposeful design of deeply coloured (thio) squaraines. Copyright © 2015 John Wiley & Sons, Ltd.