Linear Operators, Part 2 |
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Page 2013
... given by ( 9 ) and the domain of A consists precisely of those y for which the limit in ( 9 ) exists . σ ዋ Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate ...
... given by ( 9 ) and the domain of A consists precisely of those y for which the limit in ( 9 ) exists . σ ዋ Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate ...
Page 2096
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous homomorphism of 2 into B ( X ) for some B - space ...
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous homomorphism of 2 into B ( X ) for some B - space ...
Page 2376
... given , one attempts to find an operator U such that T + K = U - 1TU , in this way reducing the spectral theory of T + K to that of T. We shall see that this idea can be applied with success to a wide variety of operators and , in ...
... given , one attempts to find an operator U such that T + K = U - 1TU , in this way reducing the spectral theory of T + K to that of T. We shall see that this idea can be applied with success to a wide variety of operators and , in ...
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