Linear Operators, Part 2 |
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Page 1912
... spectral theorem for bounded self adjoint operators . This spectral theorem for self adjoint operators is not logically essential to the reading of Chapter XV but a familiarity with its meaning is helpful , since it is occasionally used ...
... spectral theorem for bounded self adjoint operators . This spectral theorem for self adjoint operators is not logically essential to the reading of Chapter XV but a familiarity with its meaning is helpful , since it is occasionally used ...
Page 1965
... spectral measure e ( ) , whose existence is asserted by the spectral theorem , has the property just mentioned ; that is , e ( σ ) 0 if σ is non - void and open . To see this we note that , since is a normal space ( 1.5.9 ) , Urysohn's ...
... spectral measure e ( ) , whose existence is asserted by the spectral theorem , has the property just mentioned ; that is , e ( σ ) 0 if σ is non - void and open . To see this we note that , since is a normal space ( 1.5.9 ) , Urysohn's ...
Page 2169
... spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator topology . To see that E is a spectral resolution for T it will therefore be sufficient to show that , for each Borel ...
... spectral measure which , in view of the Orlicz - Pettis Theorem IV.10.1 , is countably additive in the strong operator topology . To see that E is a spectral resolution for T it will therefore be sufficient to show that , for each Borel ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero