Linear Operators, Part 2 |
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Results 1-3 of 58
Page 1947
... everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , ... , B. 2 1 2 = PROOF . For Ee B1 , put F ( E ) = 1-2E . Then F ( E ) 2 I - 4E + 4E2 = I , and ...
... everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , ... , B. 2 1 2 = PROOF . For Ee B1 , put F ( E ) = 1-2E . Then F ( E ) 2 I - 4E + 4E2 = I , and ...
Page 2011
... everywhere on S but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we define the matrix ( 1 )  ̧ ( 8 ) =  ( 8 ) , SE σ , = 0 , S 8 & σ , and the operator  , in H " according to the equations ( 2 ) D (  ...
... everywhere on S but not necessarily bounded . For every set σ in Σ and every such matrix  ( s ) we define the matrix ( 1 )  ̧ ( 8 ) =  ( 8 ) , SE σ , = 0 , S 8 & σ , and the operator  , in H " according to the equations ( 2 ) D (  ...
Page 2191
... everywhere defined operator , it follows from Lemma VII.6.1 that , for sufficiently large values of m , the operators nm S ( fm ) = Σ fm ( \ , ) E ( 0 ; ) i = 1 have bounded everywhere defined inverses . This shows that , for ...
... everywhere defined operator , it follows from Lemma VII.6.1 that , for sufficiently large values of m , the operators nm S ( fm ) = Σ fm ( \ , ) E ( 0 ; ) i = 1 have bounded everywhere defined inverses . This shows that , for ...
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