Linear Operators, Part 2 |
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Page 2242
... Definition 10 , where ƒ ( z ) = z , then T is said to be an unbounded spectral operator of scalar type . The ... Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the resolution of the identity for T in the ...
... Definition 10 , where ƒ ( z ) = z , then T is said to be an unbounded spectral operator of scalar type . The ... Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the resolution of the identity for T in the ...
Page 2590
... definition of , XV.4.2 ( 1938 ) spectrum of , XV.4.3 ( 1939 ) Quasi - nilpotent part of a spectral opera- tor , definition of , XV.4.6 ( 1941 ) Radical part of a spectral operator , defini- tion of , XV.4.6 ( 1941 ) Range of a spectral ...
... definition of , XV.4.2 ( 1938 ) spectrum of , XV.4.3 ( 1939 ) Quasi - nilpotent part of a spectral opera- tor , definition of , XV.4.6 ( 1941 ) Radical part of a spectral operator , defini- tion of , XV.4.6 ( 1941 ) Range of a spectral ...
Page 2591
... definition of , XV.2.1 ( 1929 ) integral with respect to , XV.2 ( 1929 ) Spectral operator , adjoint of , XVI.4.6 ( 2148 ) , XVI.5.16 ( 2162 ) canonical reduction of , XV.4 ( 1937 ) , XV.4.5 ( 1939 ) , XVII.5.11 ( 2224 ) conditions for ...
... definition of , XV.2.1 ( 1929 ) integral with respect to , XV.2 ( 1929 ) Spectral operator , adjoint of , XVI.4.6 ( 2148 ) , XVI.5.16 ( 2162 ) canonical reduction of , XV.4 ( 1937 ) , XV.4.5 ( 1939 ) , XVII.5.11 ( 2224 ) conditions for ...
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