Linear Operators, Part 2 |
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Page 2232
... Q is closed . Let { n } be a second increasing sequence of elements of 2 such that E ( \ ) = 1 ễn ) = I , and let Q be defined by the equations n D ( Q ) = { x lim QoE ( en ) x exists } , - Qx = lim QoE ( en ) x , x = D ( Q ) . 81∞ To ...
... Q is closed . Let { n } be a second increasing sequence of elements of 2 such that E ( \ ) = 1 ễn ) = I , and let Q be defined by the equations n D ( Q ) = { x lim QoE ( en ) x exists } , - Qx = lim QoE ( en ) x , x = D ( Q ) . 81∞ To ...
Page 2250
... let q = { f ( ∞ ) } ; if ƒ is not analytic at infinity , let q be the null set . Let q ' be the open set U q . The conclusion of the theorem will be divided into two parts . ( a ) ( b ) g ( ƒ ( T ) ) | E1 ( q ) X = h ( T ) | E1 ( q ) X ...
... let q = { f ( ∞ ) } ; if ƒ is not analytic at infinity , let q be the null set . Let q ' be the open set U q . The conclusion of the theorem will be divided into two parts . ( a ) ( b ) g ( ƒ ( T ) ) | E1 ( q ) X = h ( T ) | E1 ( q ) X ...
Page 2416
... q ( A ) is similar to the operator T and is therefore a spectral operator of scalar type . PROOF . We apply Theorem 8 and Corollary 9. Let the B - space X of Theorem 8 be L , ( D , Y ) . Let A be the set of all bounded , measurable ...
... q ( A ) is similar to the operator T and is therefore a spectral operator of scalar type . PROOF . We apply Theorem 8 and Corollary 9. Let the B - space X of Theorem 8 be L , ( D , Y ) . Let A be the set of all bounded , measurable ...
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