Temat: closed ideals - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Ditkin’s condition and ideals with at most countable hull in algebras of functions analytic in the unit disc
Autorzy:: Sołtysiak, Andrzej
Wawrzyńczyk, Antoni
Powiązania:: https://bibliotekanauki.pl/articles/745506.pdf
Data publikacji:: 2012
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Closed ideals
Banach algebras
Ditkin's condition
Opis:: Agrafeuil and Zarrabi in [1] characterized all closed ideals with at most countable hull in a unital Banach algebra embedded in the classical disc algebra and satisfying certain conditions ((H1), (H2), (H3)), and the analytic Ditkin condition. We modify Ditkin’s condition and show that analogous result is true for a wider class of algebras. This is an extension of the result obtained in [1].
Źródło:: Commentationes Mathematicae; 2012, 52, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A spectral synthesis property for \(C_b(X, \Beta)\)
Autorzy:: Arizmendi-Peimbert, H.
Carrillo-Hoyo, A.
Garcı́a, A.
Powiązania:: https://bibliotekanauki.pl/articles/745757.pdf
Data publikacji:: 2008
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: spectral synthesis
strict topology
closed ideals
topological divisors of zero
Opis:: Let \((C_b (X) , \Beta)\) be the algebra of all continuous bounded real or complex valued functions defined on a completely regular Hausdorff space \(X\) with the usual algebraic operations and with the strict topology \(\Beta\). It is proved that \((C_b (X) , \Beta)\) has a spectral synthesis, i.e. every of its closed ideals is an intersection of closed maximal ideals of codimension 1. We give one necessary and two sufficient conditions over \(X\) in order that \((C_b (X) , \Beta)\) has no proper non-zero closed principal ideals. Moreover if \(X\) satisfy any of these two conditions and is also a k-space, then any non zero element of \(C_b(X)\) is invertible or a topological divisor of zero.
Źródło:: Commentationes Mathematicae; 2008, 48, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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