Linear Operators: Spectral operators |
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Page 2084
57 ( McCarthy ) Let T be a spectral operator in a complex B - spaceX satisfying the mth order condition ( * ) . If N is the radical part of T , then Nm + 2 = 0 . 58 ( McCarthy ) Let T be a spectral operator in a complex B - spaceX which ...
57 ( McCarthy ) Let T be a spectral operator in a complex B - spaceX satisfying the mth order condition ( * ) . If N is the radical part of T , then Nm + 2 = 0 . 58 ( McCarthy ) Let T be a spectral operator in a complex B - spaceX which ...
Page 2171
The symbol T is a bounded linear operator on a complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( E ; T ' ) x with & in p ( T ) .
The symbol T is a bounded linear operator on a complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( E ; T ' ) x with & in p ( T ) .
Page 2188
Let E be a spectral measure in the complex B - space X which is defined and countably additive on a o - field of subsets of a set 1 and let g be a bounded Borel measurable function defined on the complex plane .
Let E be a spectral measure in the complex B - space X which is defined and countably additive on a o - field of subsets of a set 1 and let g be a bounded Borel measurable function defined on the complex plane .
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero