Linear Operators, Part 2 |
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Page 1945
... space is equivalent to a normal operator . This theorem and other special properties of spectral operators in Hilbert space are discussed in this section . 1 LEMMA . Let G be a bounded Abelian group of operators in Hilbert space H. Then ...
... space is equivalent to a normal operator . This theorem and other special properties of spectral operators in Hilbert space are discussed in this section . 1 LEMMA . Let G be a bounded Abelian group of operators in Hilbert space H. Then ...
Page 2068
... linear space Lo . It is clear that the linear space LoL1L satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows ...
... linear space Lo . It is clear that the linear space LoL1L satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows ...
Page 2109
... linear operators on a locally convex space E. If E is complete it is seen ( Walsh [ 2 ; p . 308 ] ) that each such ... linear span of { μ ( d ) x | 8 € Σ } ; these spaces are called the cyclic ( res- pectively , real cyclic ) subspaces ...
... linear operators on a locally convex space E. If E is complete it is seen ( Walsh [ 2 ; p . 308 ] ) that each such ... linear span of { μ ( d ) x | 8 € Σ } ; these spaces are called the cyclic ( res- pectively , real cyclic ) subspaces ...
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