Linear Operators, Part 2 |
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Page 1961
... unit in M , ( B ( H ) ) is the matrix ( e ,, ) defined as p ( 7 ) eif = 0 , i #j , = b , i = j , where e is the unit in B ( S ) , that is , the identity operator in H. The symbol I will be used for the unit in XV.9 1961 THE ALGEBRAS AP AND ...
... unit in M , ( B ( H ) ) is the matrix ( e ,, ) defined as p ( 7 ) eif = 0 , i #j , = b , i = j , where e is the unit in B ( S ) , that is , the identity operator in H. The symbol I will be used for the unit in XV.9 1961 THE ALGEBRAS AP AND ...
Page 1964
... unit ê . The integral ( 15 ) a = [ _â ( s ) e ( ds ) , â €  . S maps the algebra A into a commutative B ... unit is also ê . Since eB ( , ) and  have the same unit , Corollary IX.3.10 shows that an element in  has an inverse in  if ...
... unit ê . The integral ( 15 ) a = [ _â ( s ) e ( ds ) , â €  . S maps the algebra A into a commutative B ... unit is also ê . Since eB ( , ) and  have the same unit , Corollary IX.3.10 shows that an element in  has an inverse in  if ...
Page 2078
... unit circle and such that ( ii ) k [ ƒ ( 4 ) | ≤ M † sup | ƒ ¤ › ( e1o ) | j = 0 8 for every function f analytic in a neighborhood of the unit circle . Let 2 be the set of A in B ( X ) which satisfy the inequalities ( iii ) | A ...
... unit circle and such that ( ii ) k [ ƒ ( 4 ) | ≤ M † sup | ƒ ¤ › ( e1o ) | j = 0 8 for every function f analytic in a neighborhood of the unit circle . Let 2 be the set of A in B ( X ) which satisfy the inequalities ( iii ) | A ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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