Linear Operators, Part 2 |
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Page 1912
... Chapter XV should be familiar with the elementary topics of algebra and point set topology found in Chapter I , the three basic principles of Chapter II , and the elementary properties of the theory of integration with respect to a ...
... Chapter XV should be familiar with the elementary topics of algebra and point set topology found in Chapter I , the three basic principles of Chapter II , and the elementary properties of the theory of integration with respect to a ...
Page 1913
... Chapter XV . In the following chapter it is shown just how close these three properties come to being sufficient to ensure that an operator is a spectral operator . In order to concentrate our attention on the new concepts and avoid ...
... Chapter XV . In the following chapter it is shown just how close these three properties come to being sufficient to ensure that an operator is a spectral operator . In order to concentrate our attention on the new concepts and avoid ...
Page 1915
... Chapter XX which have important applications to some of the most difficult problems of contemporary atomic physics , we give a proof independent of the earlier results of Chapter XVI . This was possible since it concerns a type of ...
... Chapter XX which have important applications to some of the most difficult problems of contemporary atomic physics , we give a proof independent of the earlier results of Chapter XVI . This was possible since it concerns a type of ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
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