Linear Operators: Spectral operators |
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Page 1938
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Page 2169
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
Page 2252
... bounded case by writing NTS runs into difficulties . The operator N , although easily seen by Lemma 2 to have a ... operator C introduced as an example in the paragraphs of discus- sion preceding Lemma 19 , we see from the discussion ...
... bounded case by writing NTS runs into difficulties . The operator N , although easily seen by Lemma 2 to have a ... operator C introduced as an example in the paragraphs of discus- sion preceding Lemma 19 , we see from the discussion ...
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