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A theorem of Gel'fand-Mazur type

100%

Pham H.

Studia Mathematica

2009

tom 191

nr 1

81-88

Denote by 𝔠 any set of cardinality continuum. It is proved that a Banach algebra A with the property that for every collection ${a_{α}: α ∈ 𝔠} ⊂ A$ there exist α ≠ β ∈ 𝔠 such that $a_{α} ∈ a_{β}A^{#}$ is isomorphic to $⨁_{i=1}^{r} (ℂ[X]/X^{d_{i}}ℂ[X]) ⊕ E$, where $d₁,...,d_{r} ∈ ℕ$, and E is either $Xℂ[X]/X^{d₀}ℂ[X]$ for some d₀ ∈ ℕ or a 1-dimensional $⨁_{i=1}^{r} ℂ[X]/X^{d_{i}}ℂ[X]$-bimodule with trivial right module action. In particular, ℂ is the unique non-zero prime Banach algebra satisfying the above condition.

Equivalences involving (p,q)-multi-norms

51%

Blasco O., Dales H., Pham H.

Studia Mathematica

2014

tom 225

nr 1

29-59

We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form $L^{r}(Ω)$, and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.

Ograniczanie wyników

2 Studia Mathematica

2 Pham H.

1 Blasco O.

1 Dales H.

1 2014

1 2009

Wyniki wyszukiwania

A theorem of Gel'fand-Mazur type

Equivalences involving (p,q)-multi-norms