Linear Operators: Spectral operators |
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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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero