Linear Operators, Part 2 |
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Page 1960
... elements of " are , by definition , the finite ordered sets x = [ x1 , xp ] of Ρ elements in H , and addition , scalar multiplication , and scalar products are defined in HP in terms of the corresponding operations in 5 by the equations ...
... elements of " are , by definition , the finite ordered sets x = [ x1 , xp ] of Ρ elements in H , and addition , scalar multiplication , and scalar products are defined in HP in terms of the corresponding operations in 5 by the equations ...
Page 2265
... elements of B each having uniform multi- plicity . For each cardinal n let E , be the supremum of those F = F with m ( F ) = n . If 0 ‡ G ≤ E , then G is the union of elements of B of multi- plicity n . Hence E , has uniform ...
... elements of B each having uniform multi- plicity . For each cardinal n let E , be the supremum of those F = F with m ( F ) = n . If 0 ‡ G ≤ E , then G is the union of elements of B of multi- plicity n . Hence E , has uniform ...
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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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