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On positive operator-valued continuous maps

Ryszard Grzaślewicz (1996)

Commentationes Mathematicae Universitatis Carolinae

In the paper the geometric properties of the positive cone and positive part of the unit ball of the space of operator-valued continuous space are discussed. In particular we show that ext-ray C + ( K , ( H ) ) = { + 1 { k 0 } 𝐱 𝐱 : 𝐱 𝐒 ( H ) , k 0 is an isolated point of K } ext 𝐁 + ...

On positive solutions for a nonlinear boundary value problem with impulse

Huseyin Bereketoglu, Aydin Huseynov (2006)

Czechoslovak Mathematical Journal

In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.

On product of projections

Mohammad Sal Moslehian (2004)

Archivum Mathematicum

An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.

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