# Masoumeh Najafi tavaniIslamic Azad University | IAU · Department of Mathematics

Masoumeh Najafi tavani

## About

17

Publications

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Introduction

**Skills and Expertise**

## Publications

Publications (17)

In this paper we study maps Si:I⟶A, Ti:I⟶B, i=1,2 on a non-empty set I into certain Banach function algebras A and B on compact Hausdorff spaces X and Y, respectively, such that for some ε>0 and all p,q∈I satisfy d(Ranπ(T1(p)T2(q)),Ranπ(S1(p)S2(q)))⩽ε‖S1(p)S2(q)‖X, where Ranπ(.) stands for the peripheral range of functions. We first prove that, und...

Let A and B be Fr�echet function algebras on the compact Hausdor�
spaces X and Y: A linear map T : A ! B is called separating, or disjointness
preserving, whenever coz(f) \ coz(g) = ∅ implies coz(Tf) \ coz(Tg) = ∅, for
f; g 2 A. Moreover, T is called biseparating if it is bijective and both T and T1
are separating. We prove that if A and B are nor...

Let A and B be Banach function algebras on compact Hausdorff spaces X and Y, respectively, and \( \rho , \tau :I\longrightarrow A\), \( S, T :I\longrightarrow B \) be maps on a non-empty set I whose ranges are closed under multiplication and contain exponential functions. In this paper, we first show that if \(\Vert S(p)\Vert _{Y}=\Vert \rho (p)\Ve...

Let X and Y be compact Hausdorff spaces, E and F be real or complex normed spaces and A(X, E) be a subspace of C(X, E). For a function f ∈ C(X, E), let coz(f) be the cozero set of f. A pair of additive maps S, T : A(X, E) −→ C(Y, F) is said to be jointly separating if coz(Tf) ∩ coz(Sg) = ∅ whenever coz(f) ∩ coz(g) = ∅. In this paper, first, we give...

Let X and Y be compact Hausdorff spaces, E be a real or complex Banach space and F be a real or complex locally convex topological vector space. In this paper we study a pair of linear operators S , T : A ( X , E ) → C ( Y , F ) from a subspace A ( X , E ) of C ( X , E ) to C ( Y , F ), which are jointly separating, in the sense that Tf and Sg have...

Let X be a compact Hausdorff space and Ω be a locally compact σ -compact space. In this paper we study (real-linear) continuous zero product preserving functionals φ:A⟶C on certain subalgebras A of the Fréchet algebra C(X,C(Ω)) . The case that φ is continuous with respect to a specified complete metric on A will also be discussed. In particular, fo...

Let $X$ and $Y$ be compact Hausdorff spaces, $E$ and $F$ be real or complex normed spaces and $A(X,E)$ be a subspace of $C(X,E)$. For a function $f\in C(X,E)$, let $\coz(f)$ be the cozero set of $f$. A pair of additive maps $S,T: A(X,E) \lo C(Y,F)$ is said to be jointly separating if $\coz(Tf)\cap \coz(Sg)=\emptyset$ whenever $\coz(f)\cap \coz(g)=...

Let A and B be two Banach function algebras and p a two variable polynomial \(p(z,w)=zw+az+bw+c\), (\(a,b,c\in {\mathbb {C}}\)). We characterize the general form of a surjection \(T: A \longrightarrow B\) which satisfies \(\mathrm{Ran}_\pi (p(Tf,Tg))\cap \mathrm{Ran}_\pi (p(f,g))\ne \emptyset , (f,g\in A\) and \(c\ne ab)\), where \(\mathrm{Ran}_\pi...

Let X and Y be locally compact Hausdorff spaces, E be a real or complex Banach space, and A(X, E) be a subspace of C 0 (X, E). In this paper we study linear operators S, T : A(X, E)−→C 0 (Y) which are jointly separating, in the sense that coz(f) ∩ coz(g) = ∅ implies that T f · Sg ≡ 0. Here coz(·) denotes the cozero set of a function. We characteriz...

Let $X$ and $Y$ be compact Hausdorff spaces, $E$ and $F$ be real or complex Banach spaces, and $A(X,E)$ be a subspace of $C(X,E)$. In this paper we study linear operators $S,T: A(X,E) \lo C(Y,F)$ which are jointly separating, in the sense that $\coz(f) \cap \coz(g) = \emptyset$ implies that $\coz(Tf) \cap \coz(Sg)=\emptyset$. Here $\coz(\cdot)$ den...

Let T : A -> B be a surjective operator between two unital semisimple commutative Banach algebras A and B with T1 = 1. We show that if T satisfies the peripheral multiplicativity condition sigma(pi) (Tf.Tg) - sigma(pi) (f.g) for all f and g in A, where sigma(pi) (f) shows the peripheral spectrum of f, then T is a composition operator in modulus on...

Let A be a normal Fréchet function algebra on a topological space X which is the projective limit of a sequence of certain Banach function algebras and satisfies Ditkin's condition. Let B be a function algebra on a topological space Y. We show that if T : A → B is a separating map, that is f.g = 0 implies T f.T g = 0, then T can be represented as T...

Let A and B be strongly regular normal Fréchet function algebras on compact Hausdorff spaces X and Y , respectively, such that the evaluation homomorphisms are continuous on A and B . Then, every biseparating map T : A → B is a weighted composition operator of the form T f = h · ( f ∘ φ ) , where φ is a homeomorphism from Y onto X and h is a nonvan...

We impose a condition on a commutative regular Fréchet algebra (A, (pm )) to ensure that A/kerpm is a Fréchet Q-algebra. This implies that if θ is an n-homomorphism on certain Fréchet algebras (A, (pm )) into semisimple commutative Fréchet algebras (B,(qm)) such that θ(kerpm) kerqm, for large enough m, then θ is continuous. We also show that if A i...

We first extend the Arens-Royden theorem to unital, commutative Fréchet algebras under certain conditions. Then, we show that if A is a uniform Fréchet algebra on X = MA, where MA is the continuous character space of A, then A does not have dense invertible group, if we impose some conditions on X. On the other hand, if A has dense invertible group...

Let X be a hemicompact k-space and A be a uniform Fréchet algebra on X. In this note, we first show that, if each element of a dense subset of A has square root in A, then A=C(X) under certain condition. Then we show that G(C(X)), the group of invertible elements of C(X), is dense in C(X) if and only if dimX, the covering dimension of X, does not e...

In 1993, M. Fragoulopoulou applied the technique of Ransford and proved that if E and F are lmc algebras such that E is a Q-algebra, F is semisimple and advertibly complete, and (E, F) is a closed graph pair, then each surjective homomorphism ϕ : E −→ F is continuous. Later on in 1996, it was shown by Akkar and Nacir that if E and F are both LFQ-al...