Introduction to the Theory of Linear Nonselfadjoint Operators

A₁ adjoint arbitrary assertion Banach space bounded linear operator bounded operator characteristic numbers closed linear hull completely continuous operator consequently converges corollary corresponding defined dissipative operator Dokl easily seen eigenvectors and associated entire function equation equivalent finite number following result formula fulfilled H₁ Hilbert space Hilbert-Schmidt operator holomorphic imaginary component inequality integral invariant with respect invertible operator kernel Lemma lemma is proved Let us denote linear hull M. G. Krein matrix nonselfadjoint operators normal eigenvalue obtain Obviously operator AE operator H operator-function orthogonal orthonormal basis orthonormal system projector PROOF properties quadratically close regular point relation root subspace root vectors s-numbers s. n. function s.n. ideal S₁ satisfies the condition selfadjoint operator sequence sp H spectrum symmetric norm system of eigenvectors system of root Theorem 5.2 theorem is proved theory unitary operator Volterra operator zero