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 2203
... subset 8 of e such that ( i ) 1 E \ xA ( 81 ) x * -xA ( e ) x * | < ɛ , E for every Borel set 8 , with 881e . To ... subsets of 4. These open and closed sets σ ( E ) form a basis for the topology in A. To see this , note that sets of the ...
... subset 8 of e such that ( i ) 1 E \ xA ( 81 ) x * -xA ( e ) x * | < ɛ , E for every Borel set 8 , with 881e . To ... subsets of 4. These open and closed sets σ ( E ) form a basis for the topology in A. To see this , note that sets of the ...
Page 2256
... subset σ of o ( T ) which is open in the relative topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z - 1e o } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) different ...
... subset σ of o ( T ) which is open in the relative topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z - 1e o } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) different ...
Page 2309
... subset of the complex plane . Let R1 be a subset of the complex plane , and ƒ a function defined in RX R1 . Let { g } be a sequence of functions defined in the set R1 . Suppose that , for each N , – N lim | z | N | ƒ ( z , w ) - Σ In ...
... subset of the complex plane . Let R1 be a subset of the complex plane , and ƒ a function defined in RX R1 . Let { g } be a sequence of functions defined in the set R1 . Suppose that , for each N , – N lim | z | N | ƒ ( z , w ) - Σ In ...
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