Given a dissipative operator \(A\) on complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give necessary and sufficient condition for an extension of to still be dissipative. As applications, describe all maximally accretive extensions strictly positive symmetric operators highly singular first-order interval.

Our first aim is to clarify the results obtained by Lidskii devoted decomposition on root vector system of non-selfadjoint operator. We use a technique entire function theory and introduce so-called Schatten–von Neumann class convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms norm, we construct sequence contours power type that contr...

for each * in X. For any Banach space X and any element * of Xt J(x) is a nonempty closed convex subset of the sphere of radius ||x|| about zero in X*. If X* is strictly convex, J is a singlevalued mapping of X into X* and is continuous from the strong topology of X to the weak* topology of X*. J is continuous in the strong topologies if and only if the norm in X is C on the complement of the o...

In this paper we consider transport equations with accretive collision operators. We characterize when the equation has a unique solution and show that in this case the solution is stable under small perturbations of the collision operator and the initial value. In one case in which there is more than one solution we show how to make a special selection of a solution, which is then stable again...

where it is assumed that the “resolvent” L, = (T + (l/n)l)-i, II = 1, 2,... exists and is defined at least on the range of the operator f C. Such a class of operators T includes all m-accretive operators (cf. Kato ] 5 I). The equations (G,) can be solved by a degree theory argument if we assume, among other things, that L, is compact and C is continuous and bounded, or that L, is continuous and...