Functional Analysis |
Contents
Preface | 1 |
Fundamentals of Normed Linear Spaces | 34 |
Bounded Linear Maps on Banach Spaces | 70 |
Copyright | |
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application approximation assume Banach space BL(H BL(X bounded bounded operator called closed subspace compact complete consider contains converges convex corresponding defined Definition denote dense differential dm(s dm(t eigenvalues elements equal equivalent example exists fact finite dimensional follows Fourier function give given Hence Hilbert space holds identity inequality infinite inner product invertible k₁ Lemma Let X limit linear functional linear map linear space linearly independent matrix measurable metric space non-zero norm normal obtain operator orthogonal projection orthonormal basis particular polynomials positive problem Proof properties prove range reflexive represented respect result satisfies scalar seen self-adjoint operator separable sequence shows solution span spectrum subsequence subset theorem u₁ uniformly unique x₁ zero