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On suprabarrelledness of c0 (Ω, X).

Manuel López Pellicer, Salvador Moll (2003)

RACSAM

Si Ω­ es un conjunto no vacío y X es un espacio normado real o complejo, se tiene que, con la norma supremo, el espacio c0 (Ω, X) formado por las funciones f : Ω­ → X tales que para cada ε > 0 el conjunto {ω ∈ Ω­ : || f(ω) || > ε} es finito es supratonelado si y sólo si X es supratonelado.

On the algebra of smooth operators

Tomasz Ciaś (2013)

Studia Mathematica

Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra L(s',s) of so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s) and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN) of s.

On the Banach-Mazur distance between continuous function spaces with scattered boundaries

Jakub Rondoš (2023)

Czechoslovak Mathematical Journal

We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Y. Gordon (1970), we show that the constant 2 appearing in the Amir-Cambern theorem may be replaced by 3 for some class of subspaces. We achieve this by showing that the Banach-Mazur distance of two function spaces is at least 3, if the height of the set of weak peak points of one of the spaces differs from the...

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