Linear Operators: Spectral operators |
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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 Ho in terms of the corresponding operations in H by the equations ...
... 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 Ho in terms of the corresponding operations in H by the equations ...
Page 2265
... elements of B each having uniform multi- plicity . For each cardinal n let En be the supremum of those Fe & 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 multiplicity n ...
... elements of B each having uniform multi- plicity . For each cardinal n let En be the supremum of those Fe & 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 multiplicity n ...
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero