Linear Operators, Part 2 |
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Page 2095
... scalar type operators also hold for their quotients . Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed ...
... scalar type operators also hold for their quotients . Although the restrictions of operators with the single valued extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed ...
Page 2106
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then 42 is a scalar type operator . Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is ...
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then 42 is a scalar type operator . Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is ...
Page 2174
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ett | t = R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ett | t = R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
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