Linear Operators: Spectral operators |
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Page 1925
... normal ) operators as developed in Chapters X and XII . The problem of extending this reduction theory to non - normal operators is one of the most important unsolved problems in the theory of linear operations . Consider , for instance ...
... normal ) operators as developed in Chapters X and XII . The problem of extending this reduction theory to non - normal operators is one of the most important unsolved problems in the theory of linear operations . Consider , for instance ...
Page 2516
... operators whose spectrum is a spectral set . Acta Sci . Math . Szeged 27 ... operators . Ukrain . Math Ž . 11 , 16-24 ( 1959 ) . ( Russian . English summary ) ... normal operators . J. London Math . Soc . 40 , 478-486 ( 1965 ) . 2 . The ...
... operators whose spectrum is a spectral set . Acta Sci . Math . Szeged 27 ... operators . Ukrain . Math Ž . 11 , 16-24 ( 1959 ) . ( Russian . English summary ) ... normal operators . J. London Math . Soc . 40 , 478-486 ( 1965 ) . 2 . The ...
Page 2538
... operators and their applications to scattering theory . Arch . Rat . Mech . Anal . 5 , 1–34 ( 1960 ) . 2 . On the ... normal operators in Hilbert spaces . Proc . Japan Acad . 37 , 464–468 ( 1961 ) . 2. Simplification of the canonical ...
... operators and their applications to scattering theory . Arch . Rat . Mech . Anal . 5 , 1–34 ( 1960 ) . 2 . On the ... normal operators in Hilbert spaces . Proc . Japan Acad . 37 , 464–468 ( 1961 ) . 2. Simplification of the canonical ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 follows from Theorem 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