Linear Operators, Part 2 |
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Page 1930
... set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if δε Σ . E ( S ) T = TE ( S ) , σ ...
... set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if δε Σ . E ( S ) T = TE ( S ) , σ ...
Page 2149
... spectral measure E * of the preceding lemma may be extended from ( T ) to a ... set is dense , then any two analytic , or even continuous , extensions of R ... spectrum is XVI.5.1 2149 OPERATORS WHOSE SPECTRA LIE IN A JORDAN CURVE.
... spectral measure E * of the preceding lemma may be extended from ( T ) to a ... set is dense , then any two analytic , or even continuous , extensions of R ... spectrum is XVI.5.1 2149 OPERATORS WHOSE SPECTRA LIE IN A JORDAN CURVE.
Page 2150
... spectrum is totally disconnected , every spectral point is contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( ...
... spectrum is totally disconnected , every spectral point is contained in a spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily small diameter . Since it is clear that every subset of the resolvent set is an ( ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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