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Alcune osservazioni sul rango numerico per operatori non lineari

Jürgen Appell, G. Conti, Paola Santucci (1999)

Mathematica Bohemica

We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by Kachurovskij (1969) for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by Rhodius (1984).

Alcune osservazioni sulle forme trilineari

Federico Bartolozzi (2003)

Bollettino dell'Unione Matematica Italiana

Si studiano, nell'ambito della teoria delle forme trilineari, le cosidette 3 -forme simmetriche, pervenendo ad un teorema di struttura utile per una possibile classificazione, ancora inesistente, di tali 3 -forme.

Algebraic and topological properties of some sets in ℓ₁

Taras Banakh, Artur Bartoszewicz, Szymon Głąb, Emilia Szymonik (2012)

Colloquium Mathematicae

For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series n = 1 x ( n ) . Guthrie and Nymann proved that E(x) is one of the following types of sets: () a finite union of closed intervals; () homeomorphic to the Cantor set; homeomorphic to the set T of subsums of n = 1 b ( n ) where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, and the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), () and ( ), respectively. We show that ℐ and are strongly -algebrable and is -lineable. We...

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