Linear Operators, Part 2 |
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Page 2308
... mapping σ → [ A1 ( o ) , ... , Am ( o ) ] is a one - to - one mapping of E. Since it maps into unitary m - space , and since the space is at least m - dimensional , it must map onto all of unitary m - space . Suppose that we can show ...
... mapping σ → [ A1 ( o ) , ... , Am ( o ) ] is a one - to - one mapping of E. Since it maps into unitary m - space , and since the space is at least m - dimensional , it must map onto all of unitary m - space . Suppose that we can show ...
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 ( f ) ( x ) = exp ( a ( x ) ) f ( ( x ) ) for each fe ...
... 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 ( f ) ( x ) = exp ( a ( x ) ) f ( ( x ) ) for each fe ...
Page 2448
... mapping ŋ : A → A , of norm at most M1 , is given ; that ( c ) a continuous linear mapping г : A · → B ( X ) , of norm at most M1 , such is defined ; Tг ( A ) — г ( A ) T = q ( A — n ( A ) ) , A € A , ( d ) a continuous bilinear ...
... mapping ŋ : A → A , of norm at most M1 , is given ; that ( c ) a continuous linear mapping г : A · → B ( X ) , of norm at most M1 , such is defined ; Tг ( A ) — г ( A ) T = q ( A — n ( A ) ) , A € A , ( d ) a continuous bilinear ...
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