Linear Operators: Spectral operators |
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Page 2078
... Prove that A1⁄2 ≤ A and that A1⁄2 ≤ A * . 27 Prove that A ≤ A + 1 . 28 Show that A ≤ A. 29 Let f ( z ) = circle . Then 2л ( k ∞ | a , z " be analytic in a neighborhood of the unit + ∞ [ ** [ ƒf ( x + 1 ) ( e1o ) | 2 d0 = 2π Σ | a ...
... Prove that A1⁄2 ≤ A and that A1⁄2 ≤ A * . 27 Prove that A ≤ A + 1 . 28 Show that A ≤ A. 29 Let f ( z ) = circle . Then 2л ( k ∞ | a , z " be analytic in a neighborhood of the unit + ∞ [ ** [ ƒf ( x + 1 ) ( e1o ) | 2 d0 = 2π Σ | a ...
Page 2152
... prove that M ( S 。) is closed . In other words , we may and shall assume that 8 is the complement of an open subinterval y of Io . Let { x } be a sequence in X , convergent to the point x , and with p ( x ) y . To prove ( C ) it will ...
... prove that M ( S 。) is closed . In other words , we may and shall assume that 8 is the complement of an open subinterval y of Io . Let { x } be a sequence in X , convergent to the point x , and with p ( x ) y . To prove ( C ) it will ...
Page 2236
... proves the first part of ( v ) . To prove the second part of ( v ) it is sufficient , since ƒ ( T ) is closed , to show that f ( T ) is everywhere defined ( cf. the closed graph theorem ( II.2.4 ) ) . By ( ii ) , D ( ƒ ( T ) ) ≥ E ( e ) ...
... proves the first part of ( v ) . To prove the second part of ( v ) it is sufficient , since ƒ ( T ) is closed , to show that f ( T ) is everywhere defined ( cf. the closed graph theorem ( II.2.4 ) ) . By ( ii ) , D ( ƒ ( T ) ) ≥ E ( e ) ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero