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 |
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