Linear Operators: Spectral operators |
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Page 2107
... ( respectively , scalar type ) operator , then T is spectral ( respectively , scalar type ) . A number of papers dealing with groups or semi - groups of spectral operators have been published . See Berkson [ 5 ] , Foias [ 3 , 8 ] ...
... ( respectively , scalar type ) operator , then T is spectral ( respectively , scalar type ) . A number of papers dealing with groups or semi - groups of spectral operators have been published . See Berkson [ 5 ] , Foias [ 3 , 8 ] ...
Page 2108
... ( respectively , Y ) to A. Then in order for there to exist a necessarily unique spectral measure A on the Baire sets ... ( respectively , positive ) in case its spectrum o ( a ) is contained in R ( respectively , [ 0 , + ∞ ) ) . It can be ...
... ( respectively , Y ) to A. Then in order for there to exist a necessarily unique spectral measure A on the Baire sets ... ( respectively , positive ) in case its spectrum o ( a ) is contained in R ( respectively , [ 0 , + ∞ ) ) . It can be ...
Page 2109
... ( respectively , MÅ ( x ) ) be the closed complex ( respectively , real ) linear span of { μ ( 8 ) x | 8 € } ; these spaces are called the cyclic ( res- pectively , real cyclic ) subspaces generated by x . It is proved that the spectral ...
... ( respectively , MÅ ( x ) ) be the closed complex ( respectively , real ) linear span of { μ ( 8 ) x | 8 € } ; these spaces are called the cyclic ( res- pectively , real cyclic ) subspaces generated by x . It is proved that the spectral ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 follows from Theorem 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