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 X 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 X on the Baire sets ... ( respectively , positive ) in case its spectrum o ( a ) is contained in R ( respectively , [ 0 , + ∞ ) ) . It can be ...
Page 2109
... ( respectively , MR ( x ) ) be the closed complex ( respectively , real ) linear span of { μ ( 8 ) x | 8 = 2 } ; these spaces are called the cyclic ( res- pectively , real cyclic ) subspaces generated by x . It is proved that the spectral ...
... ( respectively , MR ( x ) ) be the closed complex ( respectively , real ) linear span of { μ ( 8 ) x | 8 = 2 } ; 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 algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero