Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1960
... elements of Ho are , by definition , the finite ordered sets x [ x1 , ... , x , ] of p elements in H , and = addition , scalar multiplication , and scalar products are defined in " in terms of the corresponding operations in H by the ...
... elements of Ho are , by definition , the finite ordered sets x [ x1 , ... , x , ] of p elements in H , and = addition , scalar multiplication , and scalar products are defined in " in terms of the corresponding operations in H by the ...
Page 1966
... elements of the algebra  are equivalence classes where two matrices  and B are equivalent if  ( s ) = ( s ) B for e - almost all 8 in S. P p For a given matrix  = ( â ,, ) in Â3 we shall use the symbol f ̧ ( s ) e ( ds ) for the ...
... elements of the algebra  are equivalence classes where two matrices  and B are equivalent if  ( s ) = ( s ) B for e - almost all 8 in S. P p For a given matrix  = ( â ,, ) in Â3 we shall use the symbol f ̧ ( s ) e ( ds ) for the ...
Page 2512
... elements and adjoined elements of non- selfadjoint operators close to normal ones . Doklady Akad . Nauk SSSR 115 , 207-210 ( 1957 ) . ( Russian ) Math . Rev. 20 # 1227 , 205 ( 1959 ) . 2 . On the completeness of systems of eigen - elements ...
... elements and adjoined elements of non- selfadjoint operators close to normal ones . Doklady Akad . Nauk SSSR 115 , 207-210 ( 1957 ) . ( Russian ) Math . Rev. 20 # 1227 , 205 ( 1959 ) . 2 . On the completeness of systems of eigen - elements ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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