Linear Operators, Part 2 |
From inside the book
Results 1-3 of 76
Page 2094
... unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( I ) , then T has a unique resolution of the identity of class ( T ) . Moreover , ( Berkson and Dowson [ 1 ] ) , if T is spectral ...
... unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( I ) , then T has a unique resolution of the identity of class ( T ) . Moreover , ( Berkson and Dowson [ 1 ] ) , if T is spectral ...
Page 2143
... unique extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF ...
... unique extension of the adjoint E * to a spectral measure on the o - field M ( T ) of sets measurable T which is countably additive on M ( T ) in the X topology of X * . This unique extension is bounded and commutes with T * . PROOF ...
Page 2265
... unique follows easily from the distributivity . Q.E.D. 3 THEOREM . Let m be a multiplicity function on a complete Boolean algebra B of projections in a B - space X. Then there is a unique family { En } of disjoint elements in B , n ...
... unique follows easily from the distributivity . Q.E.D. 3 THEOREM . Let m be a multiplicity function on a complete Boolean algebra B of projections in a B - space X. Then there is a unique family { En } of disjoint elements in B , n ...
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