Functional Analysis, Volume 10Academic Press, 1966 - 530 pages Excellent treatment of subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. Includes detailed proofs of theorems, bibliography, and index of symbols. 1966 edition. |
Table des matières
Preface | 10 |
Orthogonal Projections and the Spectral Theorem | 20 |
Isometries and Completion of a Metric Space | 50 |
Droits d'auteur | |
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Expressions et termes fréquents
A₁ adjoint arbitrary assume B₁ Banach algebra Banach space basis bounded linear functional bounded linear transformation Cauchy sequence chapter clearly closed subspace commutes complete orthonormal set completely continuous completes the proof complex numbers conjugate space consider continuous functions convergent subsequence convex D₁ defined definition denote dense E₁ E₂ eigenvalues elements example Exercise exists finite follows functional ƒ Hence Hilbert space identity implies inequality inner product space integral isometry lemma linear transformation linearly independent M₁ M₂ mapping metric space nonzero normal transformation normed linear space notation notion open set orthogonal projection Po(A polynomials prove real numbers result satisfied scalar self-adjoint operators self-adjoint transformation sequence of points sesquilinear functional shown space and let spectral theorem spectrum subset Suppose topological space vector space verify x₁ y₁ zero α α