Linear Operators, Part 2 |
From inside the book
Results 1-3 of 42
Page 1944
... commutative B - algebra is an ideal , hence that the operator N ( m ) defined by the equation m N ( m ) = f ( n ) ( S ) Σ n = 1 Nn n ! is in the radical of the closed commutative subalgebra of 1944 XV.5.4 XV . SPECTRAL OPERATORS.
... commutative B - algebra is an ideal , hence that the operator N ( m ) defined by the equation m N ( m ) = f ( n ) ( S ) Σ n = 1 Nn n ! is in the radical of the closed commutative subalgebra of 1944 XV.5.4 XV . SPECTRAL OPERATORS.
Page 1964
... commutative B * -algebra with unit ê ( s ) = 1 for all s in S. The symbol will be used for a B * -subalgebra of eB ( S , E ) with the same unit ê . The integral ( 15 ) a = [ _â ( s ) e ( ds ) , â € Â . S maps the algebra A into a ...
... commutative B * -algebra with unit ê ( s ) = 1 for all s in S. The symbol will be used for a B * -subalgebra of eB ( S , E ) with the same unit ê . The integral ( 15 ) a = [ _â ( s ) e ( ds ) , â € Â . S maps the algebra A into a ...
Page 2179
... commutative algebras of spectral operators which are closed in the uniform operator topology . It will first be shown that such algebras A may be ... COMMUTATIVE B - ALGEBRAS 2179 The Structure of Commutative B-Algebras Spectral Operators.
... commutative algebras of spectral operators which are closed in the uniform operator topology . It will first be shown that such algebras A may be ... COMMUTATIVE B - ALGEBRAS 2179 The Structure of Commutative B-Algebras Spectral Operators.
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 other sections not shown
Other editions - View all
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