Linear Operators: Spectral operators |
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Page 2121
... unitary operator for ma + 1 . Likewise , if the resolvent satisfies as 1 | R ( X ; S ) | = O ( | 1 — | X || − 3 ) , || # 1 , B + 1 . 1 for some ẞ≥ 1 , then S is a Cm - unitary operator for m > More generally , let S € B ( X ) have σ ...
... unitary operator for ma + 1 . Likewise , if the resolvent satisfies as 1 | R ( X ; S ) | = O ( | 1 — | X || − 3 ) , || # 1 , B + 1 . 1 for some ẞ≥ 1 , then S is a Cm - unitary operator for m > More generally , let S € B ( X ) have σ ...
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 ) o ( U ) ≤ { λ = C | | λ | = 1 } , and ( iii ) | R ( λ ; U ) | ≤ | 1 − | A || −1 for AЄ p ( U ) ...
... 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 ) o ( U ) ≤ { λ = C | | λ | = 1 } , and ( iii ) | R ( λ ; U ) | ≤ | 1 − | A || −1 for AЄ p ( U ) ...
Page 2554
... unitary dilations . Bull . Acad . Polon . Sci . 12 , 37-42 ( 1964 ) . 4. Unitary dilations of contraction operators . Rozprawy Mat . 46 ( 1965 ) , 91 pp . 5. On semi - groups of contractions in Hilbert space . Studia Math . 26 , 263–272 ...
... unitary dilations . Bull . Acad . Polon . Sci . 12 , 37-42 ( 1964 ) . 4. Unitary dilations of contraction operators . Rozprawy Mat . 46 ( 1965 ) , 91 pp . 5. On semi - groups of contractions in Hilbert space . Studia Math . 26 , 263–272 ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero