Related papers: A several variables Kowalski-S\lodkowski theorem f…

This paper presents a fairly general version of the well-known Gleason-Kahane-$\dot{\text{Z}}$elazko (GKZ) theorem in the spirit of a GKZ type theorem obtained recently by Mashreghi and Ransford for Hardy spaces. In effect, we characterize…

We generalize the Gleason-Kahane-\.Zelazko theorem to modules. As an application, we show that every linear functional on a Hardy space that is non-zero on outer functions is a multiple of a point evaluation. A further consequence is that…

The Gleason-Kahane-\.Zelazko theorem states that a linear functional on a Banach algebra that is non-zero on invertible elements is necessarily a scalar multiple of a character. Recently this theorem has been extended to certain Banach…

The classical Gleason-Kahane-\.{Z}elazko Theorem states that a linear functional on a complex Banach algebra not vanishing on units, and such that $\Lambda(\mathbf 1)=1$, is multiplicative, that is, $\Lambda(ab)=\Lambda(a)\Lambda(b)$ for…

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a…

We prove, for Hermitian algebras, the multiplicative version of the Kowalski-S\l{}odkowski Theorem which identifies the characters among the collection of all complex valued functions on a Banach algebra $A$ in terms of a spectral…

We establish the following Hilbert-space analogue of the Gleason-Kahane-\.Zelazko theorem. If $\mathcal{H}$ is a reproducing kernel Hilbert space with a normalized complete Pick kernel, and if $\Lambda$ is a linear functional on…

We describe the strong dual space $({\mathcal O} (D))^*$ for the space ${\mathcal O} (D)$ of holomorphic functions of several complex variables over a bounded Lipschitz domain $D$ with connected boundary $\partial D$ (as usual, ${\mathcal…

For spaces of analytic functions defined on an open set in $\mathbb{C}^n$ that satisfy certain nice properties, we show that operators that preserve shift-cyclic functions are necessarily weighted composition operators. Examples of spaces…

We lift upper and lower estimates from linear functionals to $n$-homogeneous polynomials and using this result show that $l_\infty$ is finitely represented in the space of $n$-homogeneous polynomials, $n\ge2$, for any infinite dimensional…

This note characterizes multiplicative linear functionals on reproducing kernel Hilbert spaces of functions on the Euclidean unit ball in complex d-dimensional space, in terms of their action on kernel functions. The kernels considered are…

We establish the boundedness of the multilinear Calder\'on-Zygmund operators from a product of weighted Hardy spaces into a weighted Hardy or Lebesgue space. Our results generalize to the weighted setting results obtained by Grafakos and…

The well-known factorization theorem of Lozanovski{\u \i} may be written in the form $L^{1}\equiv E\odot E^{\prime}$, where $\odot $ means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the…

We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric…

Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calder\'on-Lozanovskii spaces are proved. We investigate assumptions on a Banach ideal space E and three…

In this paper, we extend a spherical variant of the Kowalski-S\{l}odkowski theorem due to Li, Peralta, Wang and Wang. As a corollary, we prove that every 2-local map in the set of all surjective isometries (without assuming linearity) on a…

Let $H[X]$ and $H[Y]$ be abstract Hardy spaces built upon Banach function spaces $X$ and $Y$ over the unit circle $\mathbb{T}$. We prove an analogue of the Brown-Halmos theorem for Toeplitz operators $T_a$ acting from $H[X]$ to $H[Y]$ under…

Counterexamples show that many results in the geometric function theory of one complex variable are not applicable for several complex variables. In this paper, we obtain sharp bounds for the Zalcman functional for $n=3$ associated with the…

In the present paper we give some explicit proofs for folklore theorems on holomorphic functions in several variables with values in a locally complete locally convex Hausdorff space $E$ over $\mathbb{C}$. Most of the literature on…

The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in the complex plane. The norms for these…