Linear Operators, Part 2 |
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Page 2283
... metric space and hence separable in the X - topology . Thus m ( E * ) ≤ N。 and from the definition of the projections F it is seen that E * can have no part of finite nonzero multiplicity . Q.E.D. n We shall now discuss a problem of ...
... metric space and hence separable in the X - topology . Thus m ( E * ) ≤ N。 and from the definition of the projections F it is seen that E * can have no part of finite nonzero multiplicity . Q.E.D. n We shall now discuss a problem of ...
Page 2522
... metric space of closed operators . Rend . Sem . Mat . Univ . Padova 36 , 217–222 ( 1966 ) . Coddington , E. A. ( see also Biriuk , G. ) 5. Formally normal operators having no normal extensions . Canadian J. Math . 17 , 1030-1040 ( 1965 ) ...
... metric space of closed operators . Rend . Sem . Mat . Univ . Padova 36 , 217–222 ( 1966 ) . Coddington , E. A. ( see also Biriuk , G. ) 5. Formally normal operators having no normal extensions . Canadian J. Math . 17 , 1030-1040 ( 1965 ) ...
Page 2545
... space with indefinite metric . Doklady Akad . Nauk SSSR 154 , 1023–1026 ( 1964 ) . ( Russian ) Math . Rev. 29 # 6314 , 1183 ( 1965 ) . 26. Integral equations on a half - line with kernel depending on the difference of the arguments ...
... space with indefinite metric . Doklady Akad . Nauk SSSR 154 , 1023–1026 ( 1964 ) . ( Russian ) Math . Rev. 29 # 6314 , 1183 ( 1965 ) . 26. Integral equations on a half - line with kernel depending on the difference of the arguments ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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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