Linear Operators, Part 2 |
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Page 2121
... unitary operator for ma + 1 . Likewise , if the resolvent satisfies - > 1 | R ( λ ; S ) | = O ( | 1 — | X || − 3 ) , [ x ] # 1 , B + 1 . as → 1 for some ẞ≥ 1 , then S is a Cm - unitary operator for m > More generally , let S e B ( X ) ...
... unitary operator for ma + 1 . Likewise , if the resolvent satisfies - > 1 | R ( λ ; S ) | = O ( | 1 — | X || − 3 ) , [ x ] # 1 , B + 1 . as → 1 for some ẞ≥ 1 , then S is a Cm - unitary operator for m > More generally , let S e B ( X ) ...
Page 2173
... unitary operator on X. It is easy to see that if U e B ( X ) is unitary , then ( i ) | U | = 1 for n = 0 , ± 1 , +2 , ( ii ) σ ( U ) ≤ { \ € C || λ | = 1 } , and ( iii ) | R ( λ ; U ) | ≤ | 1 — | A || -1 for λe p ( U ) . Moreover , if ...
... unitary operator on X. It is easy to see that if U e B ( X ) is unitary , then ( i ) | U | = 1 for n = 0 , ± 1 , +2 , ( ii ) σ ( U ) ≤ { \ € C || λ | = 1 } , and ( iii ) | R ( λ ; U ) | ≤ | 1 — | A || -1 for λe p ( U ) . Moreover , if ...
Page 2560
... unitary spectra . Acta Math . 106 , 215-232 ( 1961 ) . 23 . 24 . 25 . 26 . A note on non - negative matrices . Canadian J. Math . 13 , 59–62 ( 1961 ) . Absolute continuity of certain unitary and half - scattering operators . Proc . Amer ...
... unitary spectra . Acta Math . 106 , 215-232 ( 1961 ) . 23 . 24 . 25 . 26 . A note on non - negative matrices . Canadian J. Math . 13 , 59–62 ( 1961 ) . Absolute continuity of certain unitary and half - scattering operators . Proc . Amer ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero