Linear Operators, Part 2 |
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Results 1-3 of 11
Page 1951
... ideal J in B ( X ) . Then every projection E ( o ) with 0 σ belongs to 3. If 3 is closed , then S and N also belong to J. σ PROOF . Let 0 ō and let T , = TE ( 0 ) | E ( o ) X , the restriction of T to the invariant subspace E ( o ) X ...
... ideal J in B ( X ) . Then every projection E ( o ) with 0 σ belongs to 3. If 3 is closed , then S and N also belong to J. σ PROOF . Let 0 ō and let T , = TE ( 0 ) | E ( o ) X , the restriction of T to the invariant subspace E ( o ) X ...
Page 2264
... ideal if E , F D implies Ev Fe D and GE , EE D , implies Ge D. The ideal D is dense if every element of B is a union of elements of D. A o - ideal is an ideal closed under countable unions . 2 LEMMA . Let D be a dense ideal in 2264 ...
... ideal if E , F D implies Ev Fe D and GE , EE D , implies Ge D. The ideal D is dense if every element of B is a union of elements of D. A o - ideal is an ideal closed under countable unions . 2 LEMMA . Let D be a dense ideal in 2264 ...
Page 2266
... ideal in B and thus , in defining the multiplicity on B , Lemma 2 permits us to restrict our attention to C. 5 LEMMA . The set C is a dense o - ideal in B. A projection belongs to if and only if it is the carrier projection of a vector ...
... ideal in B and thus , in defining the multiplicity on B , Lemma 2 permits us to restrict our attention to C. 5 LEMMA . The set C is a dense o - ideal in B. A projection belongs to if and only if it is the carrier projection of a vector ...
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