in this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a banach algebra $a$ into a semisimple banach algebra $b$ is continuous.

and Applied Analysis 3 effectively larger than that of the ordinary conemetric spaces. That is, every cone metric space is a cone b-metric space, but the converse need not be true. The following examples show the above remarks. Example 7. Let X = {−1, 0, 1}, E = R, andP = {(x, y) : x ≥ 0, y ≥ 0}. Define d : X × X → P by d(x, y) = d(y, x) for all x, y ∈ X, d(x, x) = θ, x ∈ X, and d(−1, 0) = (3, ...

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

In this work, we first introduce almost contraction mappings for a pair of two in cone metric spaces over Banach algebras (CMSBA). Then, observe that the class such setting contains those many well known mappings. Finally, prove some fixed point theorems, and obtain $(S,T)$-stability results Jungck iterations CMSBA.

This paper contains the following results for ecohomies with infinite dimensional commodity spaces. (i) We establish a core-Walras equivalence theorem for economies with an atomless measure space of agents and with an ordered separable Banach commodity space whose positive cone has a non-empty norm interior. This result includes as a special case the Aumann (1964) and Schmeidler-Hildenbrand [Hi...

We study the exponential dichotomy of an exponentially bounded, strongly continuous cocycle over a continuous ow on a locally compact metric space acting on a Banach space X. Our main tool is the associated evolution semigroup on C 0 ((; X). We prove that the cocycle has exponential dichotomy if and only if the evolution semi-group is hyperbolic if and only if the imaginary axis is contained in...

We generalise the Riesz representation theorems for positive linear functionals on $$\text {C}_{\text {c}}(X)$$ and {0}}(X)$$ , where X is a locally compact Hausdorff space, to operators from these spaces into partially ordered vector space E. The representing measures are defined Borel $$\sigma $$ -algebra of take their values in extended cone corresponding integrals order integrals. give expl...

In this paper, we introduce and formulate the definitions of Banach operator type k and Banach operator pair on intuitionistic fuzzy metric space. Thereafter we prove some properties and theorems on intuitionistic fuzzy metric space.

The aim of this notes is to provide basic information about commutative Banach algebras. The final goal is to show that a unital, commutative complex Banach algebra A can be embedded as subalgebra of C(MA), the algebra of continuous functions on a w∗-compact setMA, known as the maximal ideal space or character space. Also, the non unital commutative complex Banach algebra can be embedded as a s...