Linear Operators: Spectral operators |
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Page 2265
... multiplicity function on B which is an extension of m on D. α α PROOF . If E = B define m ( E ) = \ / \ / a m ( Bɑ ) , where { B } is any family in D such that E ... multiplicity function for B it will XVIII.3.2 2265 MULTIPLICITY THEORY.
... multiplicity function on B which is an extension of m on D. α α PROOF . If E = B define m ( E ) = \ / \ / a m ( Bɑ ) , where { B } is any family in D such that E ... multiplicity function for B it will XVIII.3.2 2265 MULTIPLICITY THEORY.
Page 2283
... multiplicity n if and only if its adjoint E * in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E * satisfy the countable chain condition . Also since each projection is the union of projections of ...
... multiplicity n if and only if its adjoint E * in B * has finite uniform multiplicity n . PROOF . It is sufficient to suppose E and E * satisfy the countable chain condition . Also since each projection is the union of projections of ...
Page 2288
... multiplicity theory as presented in Section 3 is due to W. G. Bade [ 5 ] . J. Dieudonné [ 20 ] had previously obtained a multiplicity theory in the case where the adjoint * of the underlying Banach space is separable ( which implies the ...
... multiplicity theory as presented in Section 3 is due to W. G. Bade [ 5 ] . J. Dieudonné [ 20 ] had previously obtained a multiplicity theory in the case where the adjoint * of the underlying Banach space is separable ( which implies the ...
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