Linear Operators: Spectral operators |
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Page 1960
... elements of 5o 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 5 by the equations ...
... elements of 5o 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 5 by the equations ...
Page 1966
... elements of the algebra Âo are equivalence classes where two matrices  and B are equivalent if  ( s ) = ( s ) B for e - almost all s in S. P For a given matrix  = ( â1 , ) in Âo we shall use the symbol s ̧ ( s ) e ( ds ) for the ...
... elements of the algebra Âo are equivalence classes where two matrices  and B are equivalent if  ( s ) = ( s ) B for e - almost all s in S. P For a given matrix  = ( â1 , ) in Âo we shall use the symbol s ̧ ( 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 |
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