Linear Operators, Part 2 |
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Page 2022
... function defined on the spec- trum σ ( A ̧ ) = σ ( Â ) . We simply define the p xp matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) f ( Â ( s ) ) . ( If the roots of the minimal ...
... function defined on the spec- trum σ ( A ̧ ) = σ ( Â ) . We simply define the p xp matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) f ( Â ( s ) ) . ( If the roots of the minimal ...
Page 2410
... function defined in D x D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || - sup A ( z , z ' ) | < ∞ , 2.2'ED and let ( 4 ) be the integral operator defined by the equation ( 36 ) ( p ( 4 ) ...
... function defined in D x D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || - sup A ( z , z ' ) | < ∞ , 2.2'ED and let ( 4 ) be the integral operator defined by the equation ( 36 ) ( p ( 4 ) ...
Page 2477
... function F defined on R and vanishing at 3 ∞ can be approximated uniformly by linear combinations or products of functions of the form G ( A ) = ( λ 。— λ ) -1 , where || ≥ M. Hence , by Theorem XII.2.6 , F ( H + V ) can be ...
... function F defined on R and vanishing at 3 ∞ can be approximated uniformly by linear combinations or products of functions of the form G ( A ) = ( λ 。— λ ) -1 , where || ≥ M. Hence , by Theorem XII.2.6 , F ( H + V ) can be ...
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