Linear Operators, Part 2 |
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Page 2143
... extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF . For ...
... extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF . For ...
Page 2530
... selfadjoint extensions of J - symmetric operators with adjoint . Comm . Pure Appl . Math . 15 , 423–425 , ( 1962 ) . Gamelin , T. W. ( see also Balslev , E. ) 1. Decomposition theorems for Fredholm operators . Pacific J. Math . 15 , 97 ...
... selfadjoint extensions of J - symmetric operators with adjoint . Comm . Pure Appl . Math . 15 , 423–425 , ( 1962 ) . Gamelin , T. W. ( see also Balslev , E. ) 1. Decomposition theorems for Fredholm operators . Pacific J. Math . 15 , 97 ...
Page 2551
... adjoint extensions of a symmetric operator . Pacific J. Math . 12 , 1003-1022 ( 1962 ) . 2. Spectral measures , generalized resolvents , and functions of positive type . J. Math . Anal . Appl . 11 , 447-477 ( 1965 ) . Mackey , G. W. 4 ...
... adjoint extensions of a symmetric operator . Pacific J. Math . 12 , 1003-1022 ( 1962 ) . 2. Spectral measures , generalized resolvents , and functions of positive type . J. Math . Anal . Appl . 11 , 447-477 ( 1965 ) . Mackey , G. W. 4 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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