Linear Operators: General theory |
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Page xiii
... Spectral Theory 1. Spectral Theory in a Finite Dimensional Space 2. Exercises 3. Functions of an Operator 4. Spectral Theory of Compact Operators 5. Exercises • 6. Perturbation Theory 7. Tauberian Theory 8. Exercises • 480 482 485 487 ...
... Spectral Theory 1. Spectral Theory in a Finite Dimensional Space 2. Exercises 3. Functions of an Operator 4. Spectral Theory of Compact Operators 5. Exercises • 6. Perturbation Theory 7. Tauberian Theory 8. Exercises • 480 482 485 487 ...
Page xiv
Nelson Dunford, Jacob T. Schwartz. PART II . SPECTRAL THEORY IX . B - Algebras X. Bounded Normal Operators in Hilbert Space XI . Various Special Classes of Operators in L , XII . Unbounded Operators in Hilbert Space XIII . Ordinary ...
Nelson Dunford, Jacob T. Schwartz. PART II . SPECTRAL THEORY IX . B - Algebras X. Bounded Normal Operators in Hilbert Space XI . Various Special Classes of Operators in L , XII . Unbounded Operators in Hilbert Space XIII . Ordinary ...
Page 577
... Spectral Theory of Compact Operators It has been observed in some of the exercises in Section VI.9 that a number of linear operators of importance in analysis ... SPECTRAL THEORY OF COMPACT OPERATORS Spectral Theory of Compact Operators.
... Spectral Theory of Compact Operators It has been observed in some of the exercises in Section VI.9 that a number of linear operators of importance in analysis ... SPECTRAL THEORY OF COMPACT OPERATORS Spectral Theory of Compact Operators.
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ