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On m -sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry

Ognjen Milatovic (2004)

Commentationes Mathematicae Universitatis Carolinae

We consider a Schrödinger-type differential expression H V = * + V , where is a C -bounded Hermitian connection on a Hermitian vector bundle E of bounded geometry over a manifold of bounded geometry ( M , g ) with metric g and positive C -bounded measure d μ , and V is a locally integrable section of the bundle of endomorphisms of E . We give a sufficient condition for m -sectoriality of a realization of H V in L 2 ( E ) . In the proof we use generalized Kato’s inequality as well as a result on the positivity of u L 2 ( M ) satisfying the...

On maximal monotone operators with relatively compact range

Dariusz Zagrodny (2010)

Czechoslovak Mathematical Journal

It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator T can be approximated by a sequence of maximal monotone operators of type NI, which converge to T in a reasonable sense (in the sense of Kuratowski-Painleve convergence).

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