Nagel, R. - The spectrum of unbounded operator matrices with non-diagonal domain. To appear in: 1. Funct. Anal. Preprint 1988.R. Nagel, The spectrum of unbounded operator matrices with non-diagonal domain, J. Funct. Anal. 89, 291-302 (1990)....
Maybe more to the point, I don't have enough intuition for where the algebra ought to go. I've started by assuming that $u$ is a $\mu$-eigenvector of $K$ in $H$ (after extending showing $K$ is symmetric and extending $K$ to a map $H\to H$ by density of $V$ and compactn...
is the laplace operator. it is easy to verify that the domain \({\mathcal {d}}(s)\) of the stokes operator s is dense in the hilbert space j with the inner product of \([l^2(\omega )]^n\) , and the stokes operator s is an unbounded, self-adjoint, positive definite operator...
Here we used one of the well-known aspects of Shnol’s theorem: the spectrum is given by the closure of the set of energies for which there exists a non-trivial polynomially bounded solution satisfying the boundary condition. Since we are dealing with an unbounded potential, let us mention ...
Location of the discrete and continuous spectrum of the operator corresponding to a boundary value problem for an elliptic system of equations in an unbounded cylinder is studied. Stability of multi-dimensional travelling waves with respect to small perturbations is proved. These results allow us to ...
Let and be the Banach spaces and also be a bounded linear operator. By , we denote the range of , i.e., By , we also denote the set of all bounded linear operators on into itself. If is any Banach space and then the adjoint of is a bounded linear operator on the dual of define...
rolesinthecharacterizationandthestabilityo theSchechteressentialspectrumo unboundedoperators. c⃝2015RoyalDutchMathematicalSociety(KWG).PublishedbyElsevierB.V.Allrightsreserved. Keywords:Fredholmoperator;Measureo non-strictsingularity;Polynomialo strictsingularoperator;Schechter essentialspectrum Contents 1.Introduction...
Twitter Google Share on Facebook residual spectrum [rə′zij·ə·wəl ′spek·trəm] (mathematics) Those members λ of the spectrum of a linear operatorAon a Banach spaceXfor which (A- λI)-1,Ibeing the identity operator, is unbounded with domain not dense inX. ...
Assuming that $(X,d)$ is not compact we show that, under some natural conditions concerning the structure of the hierarchical lattice (= the tree of $d$-balls), any given closed subset $S$ of $[0,\\infty)$, which contains $0$ as an accumulation point and is unbounded if $X$ is...
Dehimi, S., Mortad, M.H.: Right (or left) invertibility of bounded and unbounded operators and applications to the spectrum of products. Complex Anal. Oper. Theory 12(3), 589–597 (2018) Article MathSciNet Google Scholar Frid, N., Mortad, M.H.: When nilpotence implies normality of...