Linear Operators: Spectral operators |
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Page 2144
... topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) = A ( od ) . It is seen , by using the above remarks , that for a fixed o the family of d for which the equation is valid is a σ - field . Thus if o is in ...
... topology of X * , and is bounded . It remains only to show that A ( o ) A ( 8 ) = A ( od ) . It is seen , by using the above remarks , that for a fixed o the family of d for which the equation is valid is a σ - field . Thus if o is in ...
Page 2203
... topology in 4. To see this , note that sets of the form { || ( T - 1A ) ( λ ) | < a } , with A in ( B ) form , by definition , a subbasis for the topology of A , and since B generates ( B ) , the sets σ ( E ) form a subbasis for the ...
... topology in 4. To see this , note that sets of the form { || ( T - 1A ) ( λ ) | < a } , with A in ( B ) form , by definition , a subbasis for the topology of A , and since B generates ( B ) , the sets σ ( E ) form a subbasis for the ...
Page 2256
... topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) different from zero is contained in an arbitrarily small ...
... topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) different from zero is contained in an arbitrarily small ...
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