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Fereshteh Sady

Publications and source records attributed to Fereshteh Sady.

9 recordsLinked to original sources
arXiv2026

Multiplicative spectral functions on some Banach function algebras

In this paper, we study multiplicative functions $\varphi \colon A \to \Bbb C$ on a natural Banach function algebra $A$ on a compact Hausdorff space $X$, such that $\varphi(f)\in \sigma(f)$ for all $f\in A$. It is shown that for certain natural Banach function algebras $A$, either $\ker(\varphi)$ is a maximal ideal of $A$ or $1\in {\rm span}({\rm ker}(\varphi))$ (that is $1=f_1+f_2+\cdots f_n$ for some $f_1,..., f_n \in {\rm ker}(\varphi)$). Then we investigate for the linearity of $\varphi$ in either of cases that $\varphi$ is continuous or $1\notin {\rm span}({\rm ker}(\varphi)$. We show that, for some natural Banach function algebras $A$, in either of these cases, there exists a point $x_0\in X$ such that $\varphi(f)=f(x_0)$ for some family of functions $f\in A$ (including those functions $f\in A$ that $\overline{f}\in A$). In particular, such a multiplicative spectral function on some Banach algebras including $C(X)$, Lipschitz algebras, Banach algebras of absolutely continuous functions on $[0,1]$ and $C^1([0,1])$ is linear and hence it is a character.

math.FA↗
arXiv2020

On 2-local diameter-preserving maps between C(X)-spaces

The 2-locality problem of diameter-preserving maps between C(X)-spaces is addressed in this paper. For any compact Hausdorff space X with at least three points, we give an example of a 2-local diameter-preserving map on C(X) which is not linear. However, we show that for first countable compact Hausdorff spaces X and Y, every 2-local diameter-preserving map from C(X) to C(Y) is linear and surjective up to constants in some sense. This yields the 2-algebraic reflexivity of isometries with respect to the diameter norms on the quotient spaces.

math.FA↗
arXiv2020

Isometries between completely regular vector-valued function spaces

In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces $A$ and $B$ of $C_0(X,E)$ and $C_0(Y,F)$ where $X$ and $Y$ are locally compact Hausdorff spaces and $E$ and $F$ are normed spaces, not assumed to be neither strictly convex nor complete. We show that for a class of normed spaces $F$ satisfying a new defined property related to their $T$-sets, such an isometry is a (generalized) weighted composition operator up to a translation. Then we apply the result to study surjective isometries between $A$ and $B$ whenever $A$ and $B$ are equipped with certain norms rather than the supremum norm. Our results unify and generalize some recent results in this context.

math.FA↗
arXiv2019

Composition in Modulus Maps on Semigroups of Continuous Functions

For locally compact Hausdorff spaces $X$ and $Y$, and function algebras $A$ and $B$ on $X$ and $Y$, respectively, surjections $T:A \longrightarrow B$ satisfying norm multiplicative condition $\|Tf\, Tg\|_Y =\|fg\|_X$, $f,g\in A$, with respect to the supremum norms, and those satisfying $\||Tf|+|Tg|\|_Y=\||f|+|g|\|_X$ have been extensively studied. Motivated by this, we consider certain (multiplicative or additive) subsemigroups $A$ and $B$ of $C_0(X)$ and $C_0(Y)$, respectively, and study surjections $T: A \longrightarrow B$ satisfying the norm condition $ρ(Tf, Tg)=ρ(f,g)$, $f,g \in A$, for some class of two variable positive functions $ρ$. It is shown that $T$ is also a composition in modulus map.

math.FA↗
arXiv2019

Additive jointly separating maps and ring homomorphisms

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 $\coz(f)\cap \coz(g)= \emptyset$. In this paper, first we give a partial description of additive jointly separating maps between certain spaces of vector-valued continuous functions (including spaces of vector-valued Lipschitz functions, absolutely continuous functions and continuously differentiable functions). Then we apply the results to characterize continuous ring homomorphisms between certain Banach algebras of vector-valued continuous functions. In particular, the results provide some generalizations of the recent results on unital homomorphisms between vector-valued Lipschitz algebras, with a different approach.

math.FA↗
arXiv2019

Lattice isomorphisms between certain sublattices of continuous functions

Let $C(X,I)$ be the lattice of all continuous functions on a compact Hausdorff space $X$ with values in the unit interval $I=[0,1]$. We show that for compact Hausdorff spaces $X$ and $Y$ and (not necessarily contain constants) sublattices $A$ and $B$ of $C(X,I)$ and $C(Y,I)$, respectively, which satisfy a certain separation property, any lattice isomorphism $φ: A \longrightarrow B$ induces a homeomorphism $μ: Y \longrightarrow X$. If, furthermore, $A$ and $B$ are closed under the multiplication, then $φ$ has a representation $φ(f)(y)=m_y(f(μ(y)))$, $f\in A$, for all points $y$ in a dense $G_δ$ subset $Y_0$ of $Y$, where each $m_y$ is a strictly increasing continuous bijection on $I$. In particular, for the case where $X$ and $Y$ are metric spaces and $A$ and $B$ are the lattices of all Lipschitz functions with values in $I$, the set $Y_0$ is the whole of $Y$.

math.FA↗
arXiv2018

Isometries on certain non-complete vector-valued function spaces

In the recent paper \cite{Hos}, surjective isometries, not necessarily linear, $T: {\rm AC}(X,E) \longrightarrow {\rm AC}(Y,F)$ between vector-valued absolutely continuous functions on compact subsets $X$ and $Y$ of the real line, has been described. The target spaces $E$ and $F$ are strictly convex normed spaces. In this paper, we assume that $X$ and $Y$ are compact Hausdorff spaces and $E$ and $F$ are normed spaces, which are not assumed to be strictly convex. We describe (with a short proof) surjective isometries $T: (A,\|\cdot\|_A) \longrightarrow (B,\|\cdot\|_B)$ between certain normed subspaces $A$ and $B$ of $C(X,E)$ and $C(Y,F)$, respectively. We consider three cases for $F$ with some mild conditions. The first case, in particular, provides a short proof for the above result, without assuming that the target spaces are strictly convex. The other cases give some generalizations in this topic. As a consequence, the results can be applied, for isometries (not necessarily linear) between spaces of absolutely continuous vector-valued functions, (little) Lipschitz functions and also continuously differentiable functions.

math.FA↗