Linear Operators: Spectral operators |
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Page 2256
... subset σ of o ( T ) which is open in the relative . 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 ) ...
... subset σ of o ( T ) which is open in the relative . 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 ) ...
Page 2257
... subsets of o ( R ) which do not contain 0. Since by assumption E ( o ; T ) | is uniformly bounded for o in K , since each compact open subset 01 of o ( R ) is either a compact open subset of o ( R ) not con- taining zero or the ...
... subsets of o ( R ) which do not contain 0. Since by assumption E ( o ; T ) | is uniformly bounded for o in K , since each compact open subset 01 of o ( R ) is either a compact open subset of o ( R ) not con- taining zero or the ...
Page 2309
... subset of the complex plane . Let R1 be a subset of the complex plane , and ƒ a function defined in Rx R1 . Let { g } be a sequence of functions defined in the set R1 . Suppose that , for each N , N lim | 2 | ~ | ƒ ( z , w ) − Ž 9 ...
... subset of the complex plane . Let R1 be a subset of the complex plane , and ƒ a function defined in Rx R1 . Let { g } be a sequence of functions defined in the set R1 . Suppose that , for each N , N lim | 2 | ~ | ƒ ( z , w ) − Ž 9 ...
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