Linear Operators: Spectral operators |
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Page 2121
... unitary operator for ma + 1 . Likewise , if the resolvent satisfies → 1 | R ( λ ; S ) | = O ( | 1 — | λ | | − 3 ) , || # 1 , as 1 for some ẞ≥ 1 , then S is a Cm - unitary operator for m > ß +1 . More generally , let S € B ( X ) have ...
... unitary operator for ma + 1 . Likewise , if the resolvent satisfies → 1 | R ( λ ; S ) | = O ( | 1 — | λ | | − 3 ) , || # 1 , as 1 for some ẞ≥ 1 , then S is a Cm - unitary operator for m > ß +1 . More generally , let S € B ( X ) have ...
Page 2173
... unitary operator on X. It is easy to see that if Ue B ( X ) is unitary , then ( i ) | U | 1 for n = 0 , 1 , ± 2 , ... , ( ii ) o ( U ) ≤ { λ € C | | X | = 1 } , and ( iii ) | R ( λ ; U ) | ≤ | 1 — | X || -1 for λe p ( U ) . Moreover ...
... unitary operator on X. It is easy to see that if Ue B ( X ) is unitary , then ( i ) | U | 1 for n = 0 , 1 , ± 2 , ... , ( ii ) o ( U ) ≤ { λ € C | | X | = 1 } , and ( iii ) | R ( λ ; U ) | ≤ | 1 — | X || -1 for λe p ( U ) . Moreover ...
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 |
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