Linear Operators: Spectral operators |
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Page 2256
... zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ... zero is contained in an arbitrarily small compact set open in the relative topology of o ( R ) . - 1 - Suppose now ...
... zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ... zero is contained in an arbitrarily small compact set open in the relative topology of o ( R ) . - 1 - Suppose now ...
Page 2325
... zero of sin ( za ) = B. Put R ( 1 ) = R ( 1 ) + 2mπ , R2 ) = R ( 2 ) + 2mπ . Taking our cue from the known form 27m + a + 21 , 2πm + x + 22 , 21 # 22 , 2π > Rz1 ≥ Rz2 ≥0 of the zeros of sin ( z — a ) — ẞ , we wish to show that for m ...
... zero of sin ( za ) = B. Put R ( 1 ) = R ( 1 ) + 2mπ , R2 ) = R ( 2 ) + 2mπ . Taking our cue from the known form 27m + a + 21 , 2πm + x + 22 , 21 # 22 , 2π > Rz1 ≥ Rz2 ≥0 of the zeros of sin ( z — a ) — ẞ , we wish to show that for m ...
Page 2462
... zero and { CT } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . - ... " PROOF . The set K = C ( { x = H || x | ≤ 1 } ) is ...
... zero and { CT } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . - ... " PROOF . The set K = C ( { x = H || x | ≤ 1 } ) is ...
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