Linear Operators: Spectral operators |
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Page 1957
... spectrum of S. since , according to Theorem 3 , S. , being of finite type , has no residual spectrum . Q.E.D. In Theorem 3 the requirement that the spectral operator be of finite type is quite essential . The following elementary ...
... spectrum of S. since , according to Theorem 3 , S. , being of finite type , has no residual spectrum . Q.E.D. In Theorem 3 the requirement that the spectral operator be of finite type is quite essential . The following elementary ...
Page 2258
... spectrum o ( S ) which is the disjoint union of a finite set { λ1 , ... , λn } of points and of a set which is contained ... spectrum { 1 , ... , An } lends no essential com- plication to the situation at hand , so that , without loss of ...
... spectrum o ( S ) which is the disjoint union of a finite set { λ1 , ... , λn } of points and of a set which is contained ... spectrum { 1 , ... , An } lends no essential com- plication to the situation at hand , so that , without loss of ...
Page 2565
... essential spectrum . Bull . Amer . Math . Soc . 71 , 365-367 ( 1965 ) . 2. On the essential spectrum of an arbitrary operator I. J. Math . Anal . Appl . 13 , 205-215 ( 1966 ) . Schreiber , M. 2. Unitary dilations of operators . Duke ...
... essential spectrum . Bull . Amer . Math . Soc . 71 , 365-367 ( 1965 ) . 2. On the essential spectrum of an arbitrary operator I. J. Math . Anal . Appl . 13 , 205-215 ( 1966 ) . Schreiber , M. 2. Unitary dilations of operators . Duke ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 follows from Theorem 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