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Displaying 161 – 180 of 314

Norm conditions for uniform algebra isomorphisms

Aaron Luttman, Scott Lambert (2008)

Open Mathematics

In recent years much work has been done analyzing maps, not assumed to be linear, between uniform algebras that preserve the norm, spectrum, or subsets of the spectra of algebra elements, and it is shown that such maps must be linear and/or multiplicative. Letting A and B be uniform algebras on compact Hausdorff spaces X and Y, respectively, it is shown here that if λ ∈ ℂ / 0 and T: A → B is a surjective map, not assumed to be linear, satisfying $∥T (f) T (g) + λ∥ = ∥f g + λ∥ \forall f, g \in A,$ then T is an ℝ-linear isometry and there exist an...

Normed algebras of differentiable functions on compact plane sets: completeness and semisimple completions

Heiko Hoffmann (2011)

Studia Mathematica

We continue the study of the completeness and completions of normed algebras of differentiable functions Dⁿ(K) (where K is a perfect, compact plane set), initiated by Bland, Dales and Feinstein [Studia Math. 170 (2005) and Indian J. Pure Appl. Math. 41 (2010)]. We prove new characterizations of the completeness of D¹(K) and results concerning the semisimplicity of the completion of D¹(K). In particular, we prove that semi-rectifiability is necessary for the completion of D¹(K) to be semisimple in...

On a covering group theorem and its applications.

Grigorian, S.A., Gumerov, R.N. (2002)

Lobachevskii Journal of Mathematics

On $a$ -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

If $X$ is a Tychonoff space, $C (X)$ its ring of real-valued continuous functions. In this paper, we study non-essential ideals in $C (X)$ . Let $a$ be a infinite cardinal, then $X$ is called $a$ -Kasch (resp. $\bar{a}$ -Kasch) space if given any ideal (resp. $z$ -ideal) $I$ with $gen (I) < a$ then $I$ is a non-essential ideal. We show that $X$ is an $ℵ_{0}$ -Kasch space if and only if $X$ is an almost $P$ -space and $X$ is an $ℵ_{1}$ -Kasch space if and only if $X$ is a pseudocompact and almost $P$ -space. Let $C_{F} (X)$ denote the socle of $C (X)$ . For a topological space $X$ with only...

On a New Segal Algebra.

Hans G. Feichtinger (1981)

Monatshefte für Mathematik

On an Estimate of Axler and Shapiro.

T.W. Gamelin (1985)

Mathematische Annalen

On Banach algebras satisfying a spectral maximum principle

E. Vesentini (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On certain products of Banach algebras with applications to harmonic analysis

Mehdi Sangani Monfared (2007)

Studia Mathematica

Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product $A \times_{θ} B$ , which is a strongly splitting Banach algebra extension of B by A. We obtain characterizations of bounded approximate identities, spectrum, topological center, minimal idempotents, and study the ideal structure of these products. By assuming B to be a Banach algebra in ₀(X) whose spectrum can be identified with X, we apply our results to harmonic analysis, and study the question of spectral synthesis,...

On completeness with respect to a Carathéodory-like metric

M. A. Selby (1978)

Colloquium Mathematicae

On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem

Jorma Arhippainen, Jukka Kauppi (2013)

Studia Mathematica

We develop the theory of Segal algebras of commutative C*-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand-Naimark Theorem. As an application, we describe faithful principal ideals of C*-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.

On Discontinuous Homomorphisms of L1(G).

Kjeld B. Laursen (1972)

Mathematica Scandinavica

On essential sets of function algebras in terms of their orthogonal measures

Jan Čerych (1995)

Commentationes Mathematicae Universitatis Carolinae

In the present note, we characterize the essential set of a function algebra defined on a compact Hausdorff space $X$ in terms of its orthogonal measures on $X$ .

We introduce and examine the notion of dense weak openness. In particular we show that multiplication in C(X) is densely weakly open whenever X is an interval in ℝ.

Currently displaying 161 – 180 of 314

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Displaying 161 – 180 of 314

Norm conditions for uniform algebra isomorphisms

Normed algebras of differentiable functions on compact plane sets: completeness and semisimple completions

On a covering group theorem and its applications.

On $a$ -Kasch spaces

On a New Segal Algebra.

On an Estimate of Axler and Shapiro.

On Banach algebras satisfying a spectral maximum principle

On certain products of Banach algebras with applications to harmonic analysis

On completeness with respect to a Carathéodory-like metric

On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem

On Discontinuous Homomorphisms of L1(G).

On essential sets of function algebras in terms of their orthogonal measures

On functional representation of locally $m$ -pseudoconvex algebras.

On Liouville F-Algebras

On maximal and complete regions

On maximal ideals in commutative m-convex algebras

On multiplication in spaces of continuous functions

On neighborhoods of the Kuratowski imbedding beyond the first extremum of the diameter functional

On Relative Commutants in Tensor Products of C*-algebras.

On ring derivations and quadratic functionals.

Currently displaying 161 – 180 of 314