‎ 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 $ILip_J (X,E)$.

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. ...

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

We obtain a complete description of closed ideals of the algebra D ∩ lip α , 0 < α ≤ 1 2 , where D is the Dirichlet space and lip α is the algebra of analytic functions satisfying the Lipschitz condition of order α.

Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior. Functions from A(D) act on the set of all contraction operators (‖A‖ 1) on Hilbert spaces. It is proved that the following classes of functions from A(D) coincide: (1) the class of operator Lipschitz functions on the unit circle T; (2) the class of operator Lipschitz functions...

‎In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.

The well-known Lawvere category [0,∞] of extended real positive numbers comes with a monoidal closed structure where the tensor product is the sum. But [0,∞] has another such structure, given by multiplication, which is *-autonomous and a CL-algebra (linked with classical linear logic). Normed sets, with a norm in [0,∞], inherit thus two symmetric monoidal closed structures, and categories enri...