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Let $mathfrak{n}$ be a nonempty, proper, convex subset of $mathbb{C}$. The $mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $mathfrak{n}$ and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $mathfrak{n}$-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
We present a new sufficient condition under which a maximal monotone operator $T:Xtos X^*$ admits a unique maximal monotone extension to the bidual $widetilde T:X^{**} rightrightarrows X^*$. For non-linear operators this condition is equivalent to un
Let $G$ be a compact Lie group acting smoothly on a smooth, compact manifold $M$, let $P in psi^m(M; E_0, E_1)$ be a $G$--invariant, classical pseudodifferential operator acting between sections of two vector bundles $E_i to M$, $i = 0,1$, and let $a
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. A reduced graph $G$ is said to be maximal if any reduced graph contain
We study the class of all finite directed graphs up to primitive positive constructability. The resulting order has a unique greatest element, namely the graph $P_1$ with one vertex and no edges. The graph $P_1$ has a unique greatest lower bound, nam
In a recent paper in Journal of Convex Analysis the authors studied, in non-reflexive Banach spaces, a class of maximal monotone operators, characterized by the existence of a function in Fitzpatricks family of the operator which conjugate is above t