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Concave iteration semigroups of linear continuous set-valued functions

100%

Smajdor A., Smajdor W.

Open Mathematics

2012

tom 10

nr 6

2272-2282

Let {F t: t ≥ 0} be a concave iteration semigroup of linear continuous set-valued functions defined on a convex cone K with nonempty interior in a Banach space X with values in cc(K). If we assume that the Hukuhara differences F 0(x) − F t (x) exist for x ∈ K and t > 0, then D t F t (x) = (−1)F t ((−1)G(x)) for x ∈ K and t ≥ 0, where D t F t (x) denotes the derivative of F t (x) with respect to t and $$G(x) = \mathop {\lim }\limits_{s \to 0} {{\left( {F^0 \left( x \right) - F^s \left( x \right)} \right)} \mathord{\left/ {\vphantom {{\left( {F^0 \left( x \right) - F^s \left( x \right)} \right)} {\left( { - s} \right)}}} \right. \kern-\nulldelimiterspace} {\left( { - s} \right)}}$$ for x ∈ K.

Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators

84%

Kanigowski A., Kryszewski W.

Open Mathematics

2012

tom 10

nr 6

2240-2263

We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into the underlying space.

Ograniczanie wyników

2 Open Mathematics

1 Kanigowski A.

1 Kryszewski W.

1 Smajdor A.

1 Smajdor W.

2 2012

Wyniki wyszukiwania

Concave iteration semigroups of linear continuous set-valued functions

Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators