Linear Operators: Spectral operators |
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Page 2197
... indices a such that E11 = 2 , and | E。x − y | ≤ ε . If a ≥ α1 , i = 1 , ... , n , then Ea y = y . Thus , since E , E。= Eα it follows that , for a α , - | E。x — E。x | ≤ | E ̧ x − y | + │y — E。x | α - α - αι = | E 。( E 。 x ...
... indices a such that E11 = 2 , and | E。x − y | ≤ ε . If a ≥ α1 , i = 1 , ... , n , then Ea y = y . Thus , since E , E。= Eα it follows that , for a α , - | E。x — E。x | ≤ | E ̧ x − y | + │y — E。x | α - α - αι = | E 。( E 。 x ...
Page 2358
... indices i , the inequality ( ii ) gives us an immediate bound for the function ƒ ( μ ) = R ( μ ; T + P ) ƒ = B ( μ ) ƒ in all but a finite number of the sets V1 . By the maximum modulus principle this entire function has the same ...
... indices i , the inequality ( ii ) gives us an immediate bound for the function ƒ ( μ ) = R ( μ ; T + P ) ƒ = B ( μ ) ƒ in all but a finite number of the sets V1 . By the maximum modulus principle this entire function has the same ...
Page 2552
... indices and the spectrum of certain linear operators . Akad . Nauk Armjan . SSR Dokl . 34 , 49-55 ( 1962 ) . ( Russian . Armenian summary ) Math . Rev. 27 # 6126 , 1170 ( 1964 ) . 2 . On the invariance of the spectrum of small ...
... indices and the spectrum of certain linear operators . Akad . Nauk Armjan . SSR Dokl . 34 , 49-55 ( 1962 ) . ( Russian . Armenian summary ) Math . Rev. 27 # 6126 , 1170 ( 1964 ) . 2 . On the invariance of the spectrum of small ...
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