More on Lie Derivations of Generalized Matrix Algebras

Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation to be proper. Our approach not only provides a direct proof for some known results in the theory, but also it presents several sufficient conditions assuring the properness of Lie derivations on certain generalized matrix algebras.Comment: 11 page

Lifting derivations and n−n-weak amenability of the second dual of a Banach algebra

We show that for $n\geq 2$ the $n-$weak amenability of the second dual \A^{**} of a Banach algebra \A implies that of \A. We also provide a positive answer for the case $n=1,$ which sharpens some older results. Our method of proof also provides a unified approach to give short proofs for some known results in the case where $n=1$.Comment: 8 page

Reiter's properties for the actions of locally compact quantum groups on von Neumann algebras

The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter's conditions for such an action are discussed. Several applications to some specific actions related to certain representations and corepresentaions are presented.Comment: 13 pages, To appear in Bull. Iranian Math. So

Lie derivations on trivial extension algebras

In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be decomposed into the sum of a derivation and a center valued map. We extend some known results on the properness of Lie derivations of triangular algebras. Some illuminating examples are also included.Comment: 9 page

Are Cold Dynamical Dark Energy Models Distinguishable in the Light of the Data?

In this paper we obtain observational constraints on three dynamical cold dark energy models ,include PL , CPL and FSL, with most recent cosmological data and investigate their implication for structure formation, dark energy clustering and abundance of CMB local peaks. From the joint analysis of the CMB temperature power spectrum from observation of the Planck, SNIa light-curve, baryon acoustic oscillation, $f\sigma_8$ for large scale structure observations and the Hubble parameter, the PL model has the highest growth of matter density, $\Delta_{m}$, and matter power spectrum, $P(k)$, compared to $\Lambda$CDM and other models. For the CPL on the other hand, the structure formation is considerably suppressed while the FSL has behavior similar to standard model of cosmology. Studying the clustering of dark energy, $\Delta_{DE}$, yields positive but small value with maximum of $\Delta_{DE}\simeq10^{-3}$ at early time due to matter behaviour of the PL, while for the CPL and FSL cross $\Delta_{DE}=0$ several time which demonstrate void of dark energy with $\Delta_{DE}\simeq-10^{-11}$ in certain periods of the history of dark energy evolution. Among these three models, the PL model demonstrate that is more compatible with $f\sigma_{8}$ data. We also investigated a certain geometrical measure, namely the abundance of local maxima as a function of threshold for three DDE models and find that the method is potentially capable to discriminate between the models, especially far from mean threshold. The contribution of PL and CPL for late ISW are significant compared to cosmological constant and FSL model. The tension in the Hubble parameters is almost alleviated in the PL model

Improvement Tracking Dynamic Programming using Replication Function for Continuous Sign Language Recognition

In this paper we used a Replication Function (R. F.)for improvement tracking with dynamic programming. The R. F. transforms values of gray level [0 255] to [0 1]. The resulting images of R. F. are more striking and visible in skin regions. The R. F. improves Dynamic Programming (D. P.) in overlapping hand and face. Results show that Tracking Error Rate 11% and Average Tracked Distance 7% reducedComment: 5 pages, 13 figures, Published with "International Journal of Engineering Trends and Technology (IJETT)

The higher duals of certain class of Banach algebras

Given a Banach space $A$ and fix a non-zero $\varphi\in A^*$ with $\|\varphi\|\leq 1$. Then the product $a\cdot b=\langle\varphi, a\rangle\ b$ turning $A$ into a Banach algebra which will be denoted by $_\varphi A.$ Some of the main properties of $_\varphi A$ such as Arens regularity, $n$-weak amenability and semi-simplicity are investigated.Comment: 6 page

Character Inner Amenability of Certain Banach Algebras

Character inner amenability for certain class of Banach algebras consist of projective tensor product $A\hat{\otimes}B$, Lau product $A\times_\theta B$ and module extension $A\oplus X$ are investigated. Some illuminating examples are also included.Comment: 9 page

Weighted semigroup measure algebra as a WAP-algebra

Banach algebra A for which the natural embedding x into x^ of A into WAP(A)* is bounded below; that is, for some m in R with m > 0 we have ||x^|| > m ||x||, is called a WAP-algebra. Through we mainly concern with weighted measure algebra M_b(S;w); where w is a weight on a semi-topological semigroup S. We study those con- ditions under which M_b(S;w) is a WAP-algebra (respectively dual Banach algebra). In particular, M_b(S) is a WAP-algebra (respectively dual Banach algebra) if and only if wap(S) separates the points of S (respectively S is compactly cancellative semigroup). We apply our results for improving some older results in the case where S is discrete

Arens regularity of certain weighted semigroup algebras and countability

It is known that every countable semigroup admits a weight w for which the semigroup algebra l_1(S,w) is Arens regular and no uncountable group admits such a weight; see [4]. In this paper, among other things, we show that for a large class of semigroups, the Arens regularity of the weighted semigroup algebra l_1(S,w) implies the countability of S