Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2308
... mapping σ → [ 41 ( σ ) , ... , Am ( o ) ] is a one - to - one mapping of Σ . Since it maps Σ into unitary m - space , and since the space Σ is at least m - dimensional , it must map onto all of unitary m - space . Suppose that we can ...
... mapping σ → [ 41 ( σ ) , ... , Am ( o ) ] is a one - to - one mapping of Σ . Since it maps Σ into unitary m - space , and since the space Σ is at least m - dimensional , it must map onto all of unitary m - space . Suppose that we can ...
Page 2447
... mapping the interval [ 0 , 1 ] into itself . Let be the inverse of the mapping 4. Let a ( x ) be a complex valued function with two continuous derivatives defined in [ 0 , 1 ] . Put ( Țƒ ) ( x ) = exp ( a ( x ) ) f ( ( x ) ) for each ƒe ...
... mapping the interval [ 0 , 1 ] into itself . Let be the inverse of the mapping 4. Let a ( x ) be a complex valued function with two continuous derivatives defined in [ 0 , 1 ] . Put ( Țƒ ) ( x ) = exp ( a ( x ) ) f ( ( x ) ) for each ƒe ...
Page 2448
... mapping ŋ : A → A , of norm at most M1 , is given ; that ( c ) a continuous linear mapping П : A → B ( X ) , of norm at most M1 , such is defined ; Tr ( A ) -T ( A ) T = q ( An ( A ) ) , A € A , ( d ) a continuous bilinear mapping ( A ...
... mapping ŋ : A → A , of norm at most M1 , is given ; that ( c ) a continuous linear mapping П : A → B ( X ) , of norm at most M1 , such is defined ; Tr ( A ) -T ( A ) T = q ( An ( A ) ) , A € A , ( d ) a continuous bilinear mapping ( A ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ 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