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Page 1921
Nelson Dunford, Jacob T. Schwartz. Contents PART III . SPECTRAL OPERATORS XV . Spectral Operators 1925 1 . Introduction 2. Terminology and Preliminary Notions 3. The Resolvent of a Spectral Operator 1925 1928 • 1933 4. The Canonical ...
Nelson Dunford, Jacob T. Schwartz. Contents PART III . SPECTRAL OPERATORS XV . Spectral Operators 1925 1 . Introduction 2. Terminology and Preliminary Notions 3. The Resolvent of a Spectral Operator 1925 1928 • 1933 4. The Canonical ...
Page 2094
... spectral operator and Y is a closed subspace invariant under T , then the operator T2 ( defined on X / Y by T1 [ x ] = [ Tx ] ) is a spectral operator if and only if is invariant under the resolution of the 2094 XV.16 XV . SPECTRAL ...
... spectral operator and Y is a closed subspace invariant under T , then the operator T2 ( defined on X / Y by T1 [ x ] = [ Tx ] ) is a spectral operator if and only if is invariant under the resolution of the 2094 XV.16 XV . SPECTRAL ...
Page 2118
... operator T defined by ( Tf ) ( t ) = tf ( t ) , te [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) f ) ( t ) = q ( t ) f ( t ) for q € C ° . Ф , It is proved ( see Foiaş [ 9 2118 XV.16 XV . SPECTRAL ...
... operator T defined by ( Tf ) ( t ) = tf ( t ) , te [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) f ) ( t ) = q ( t ) f ( t ) for q € C ° . Ф , It is proved ( see Foiaş [ 9 2118 XV.16 XV . SPECTRAL ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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