Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 84
Page 2241
... subset of the domain of T ( 1 / ƒ ) and vice versa . If x is in D ( T ( ƒ ) ) , then x = T ( 1 / ƒ ) 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 / ƒ ) 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 ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of σ ( 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 ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of σ ( 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 σ 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 σ of o ( R ) is either a compact open subset of o ( R ) not con- taining zero or the complement ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero