Functional Analysis and Linear Operator Theory |
Contents
Linear Algebra and Analysis | 1 |
Linear Mappings and Operators | 65 |
Compact Operators | 99 |
Copyright | |
7 other sections not shown
Common terms and phrases
adjoint B₁ Banach space bounded Cauchy sequence choose Clearly closed set compact operator compact set complex number continuous function Corollary countable defined denote dense in H diagonalizable discussion E₁ eigenspace eigenvalue eigenvector equation Exercises 4.2 finite dimensional fixed follows function ƒ given ɛ Hamel basis hence Hilbert space implies infinite inner product space integral invertible Lč(R LČ(dx LČ(R LČ[a Lemma Let H linear manifold linear map linear operator linear subspace linearly independent matrix non-zero normal operator normed space null space operator on H orthogonal projection orthonormal basis orthonormal set Pn(t polynomial problem projection of H Proof prove real numbers real-valued recall scalars Section 2.4 self-adjoint operator space and let space H spectral theorem spectrum subset subspace of H Suppose unit ball unitary operator v₁ vector space weakly convergent zero vector