SOME PROPERTIES ON FLM ALGEBRAS

Some properties of nilpotent Lie algebras

In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.

Some Properties of Vector-valued Lipschitz Algebras

‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.

A class of new results in FLM algebras

In this paper, we first derive some results by using the Gelfand spectrum and spectrum in FLM algebras. Then, the characterizations of multiplicative linear mappings are also discussed in these algebras.

Some P-Properties for Nonlinear Transformations on Euclidean Jordan Algebras

A real square matrix is said to be a P-matrix if all its principal minors are positive. It is well known that this property is equivalent to: the nonsign-reversal property based on the componentwise product of vectors, the order P-property based on the minimum and maximum of vectors, uniqueness property in the standard linear complementarity problem, (Lipschitzian) homeomorphism property of the...

Some properties of index of Lie algebras