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1
Content available remote

Multiplicative functionals and entire functions, II

100%
Jarosz K.
Studia Mathematica
|
1997
|
tom 124
|
nr 2
193-198
EN
Let A be a complex Banach algebra with a unit e, let F be a nonconstant entire function, and let T be a linear functional with T(e)=1 and such that T∘F: A → ℂ is nonsurjective. Then T is multiplicative.
2
Content available remote

Almost multiplicative functionals

100%
Jarosz K.
Studia Mathematica
|
1997
|
tom 124
|
nr 1
37-58
EN
A linear functional F on a Banach algebra A is almost multiplicative if |F(ab) - F(a)F(b)| ≤ δ∥a∥ · ∥b∥ for a,b ∈ A, for a small constant δ. An algebra is called functionally stable or f-stable if any almost multiplicative functional is close to a multiplicative one. The question whether an algebra is f-stable can be interpreted as a question whether A lacks an almost corona, that is, a set of almost multiplicative functionals far from the set of multiplicative functionals. In this paper we discuss f-stability for general uniform algebras; we prove that any uniform algebra with one generator as well as some algebras of the form R(K), K ⊂ ℂ, and A(Ω), $Ω ⊂ ℂ^{n}$, are f-stable. We show that, for a Blaschke product B, the quotient algebra $H^{∞}/BH^{∞}$ is f-stable if and only if B is a product of finitely many interpolating Blaschke products.
3
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Riemann mapping theorem in ℂⁿ

100%
Jarosz K.
Annales Polonici Mathematici
|
2012
|
tom 106
|
nr 1
199-206
EN
The classical Riemann Mapping Theorem states that a nontrivial simply connected domain Ω in ℂ is holomorphically homeomorphic to the open unit disc 𝔻. We also know that "similar" one-dimensional Riemann surfaces are "almost" holomorphically equivalent. We discuss the same problem concerning "similar" domains in ℂⁿ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem
4
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Multiplicative functionals and entire functions

100%
Jarosz K.
Studia Mathematica
|
1996
|
tom 119
|
nr 3
289-297
EN
Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.
5
Content available remote

Wiesław Żelazko, topological algebras, Banach algebras

100%
Jarosz K.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
9-20
6
Content available remote

Small deformations of topological algebras

64%
Abel M., Jarosz K.
Studia Mathematica
|
2003
|
tom 156
|
nr 3
203-226
EN
We investigate stability of various classes of topological algebras and individual algebras under small deformations of multiplication.
7
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Automatic continuity of biseparating maps

64%
Araujo J., Jarosz K.
Studia Mathematica
|
2003
|
tom 155
|
nr 3
231-239
EN
We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.
8
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Noncommutative uniform algebras

64%
Abel M., Jarosz K.
Studia Mathematica
|
2004
|
tom 162
|
nr 3
213-218
EN
We show that a real Banach algebra A such that ||a²|| = ||a||² for a ∈ A is a subalgebra of the algebra $C_{ℍ}(X)$ of continuous quaternion-valued functions on a compact set X.
9
Content available remote

Topological algebras in which all maximal two-sided ideals are closed

64%
Abel M., Jarosz K.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
35-43
EN
We characterize unital topological algebras in which all maximal two-sided ideals are closed.
10
Content available remote

Multipliers in complex Banach spaces and structure of the unit balls

44%
Jarosz K.
Studia Mathematica
|
1987
|
tom 87
|
nr 3
197-213
11
Content available remote

A generalization of the Banach-Stone theorem

26%
Jarosz K.
Studia Mathematica
|
1982
|
tom 73
|
nr 1
33-39
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