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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Results 1-3 of 90
Page 2241
... subset of the domain of T ( 1 / ƒ ) and vice versa . If x is in D ( T ( ƒ ) ) , then x = T ( 1 / f ) T ( ƒ ) x , and so x is in the range R ( T ( 1 / ƒ ) ) of T ( 1 / f ) . Thus R ( T ( 1 / ƒ ) ) = D ( T ( ƒ ) ) . The equation R ( T ( ƒ ) ...
... subset of the domain of T ( 1 / ƒ ) and vice versa . If x is in D ( T ( ƒ ) ) , then x = T ( 1 / f ) T ( ƒ ) x , and so x is in the range R ( T ( 1 / ƒ ) ) of T ( 1 / f ) . Thus R ( T ( 1 / ƒ ) ) = D ( T ( ƒ ) ) . The equation R ( T ( ƒ ) ...
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 | z1 e σ } 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 | z1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) different ...
Page 2257
... subsets of o ( R ) which do not contain 0. Since by assumption ( o ; T ) | is uniformly bounded for σ in K , since each compact open subset 01 of o ( R ) is either a compact open subset of o ( R ) not con- taining zero or the complement ...
... subsets of o ( R ) which do not contain 0. Since by assumption ( o ; T ) | is uniformly bounded for σ in K , since each compact open subset 01 of o ( R ) is either a compact open subset of o ( R ) not con- taining zero or the complement ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero