Linear Operators, Part 2 |
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Page 2094
... subspace X and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple ...
... subspace X and one of its complements ( that is , if T commutes with some projection of X onto Y ) , then the restriction T | Y of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple ...
Page 2113
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace of a B - space to be a spectral maximal subspace of T = B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace of a B - space to be a spectral maximal subspace of T = B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
Page 2114
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if σ is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if σ is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then EX is a spectral maximal subspace of T. Hence both ...
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