Linear Operators: Spectral operators |
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Page 2256
... Suppose that o ( T ) is totally disconnected . Then T is a spectral operator if and only if ( a ) the family of projections E ( o ; T ) corresponding to compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X ...
... Suppose that o ( T ) is totally disconnected . Then T is a spectral operator if and only if ( a ) the family of projections E ( o ; T ) corresponding to compact spectral sets of T is uniformly bounded , and ( b ) no non - zero x in X ...
Page 2284
... suppose the sets en are disjoint and Un = 1 en = P , the whole plane . = n סא ... " * 1 , ... , xn * Now consider n fixed and suppose En 0. It follows from Lemma 18 and Theorem 19 that there exist vectors x1 , x and functions x1 , such ...
... suppose the sets en are disjoint and Un = 1 en = P , the whole plane . = n סא ... " * 1 , ... , xn * Now consider n fixed and suppose En 0. It follows from Lemma 18 and Theorem 19 that there exist vectors x1 , x and functions x1 , such ...
Page 2303
... Suppose that E is its resolution of the identity , and suppose that { n } is an enumeration of its spectrum . Let d , denote the distance from λ , to o ( T ) — { \ n } . Suppose that for all but a finite number of n , E ( ^ „ ) has a ...
... Suppose that E is its resolution of the identity , and suppose that { n } is an enumeration of its spectrum . Let d , denote the distance from λ , to o ( T ) — { \ n } . Suppose that for all but a finite number of n , E ( ^ „ ) has a ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator 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 operators 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 sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero