Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 87
Page 2257
... compact spectral set o of T. Moreover , it is clear that as σ runs over the family K of all compact open subsets of σ ( T ) , 7 ( σ ) runs over the family of all compact open subsets of o ( R ) which do not contain 0. Since by ...
... compact spectral set o of T. Moreover , it is clear that as σ runs over the family K of all compact open subsets of σ ( T ) , 7 ( σ ) runs over the family of all compact open subsets of o ( R ) which do not contain 0. Since by ...
Page 2357
... compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) of the theorem , we may consequently pass from ... compact , it follows from Lemma VI.5.3 that for v > 0 the operator ( T — λ 。 I ) - ' is compact . Thus , if v > 0 , then ...
... compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) of the theorem , we may consequently pass from ... compact , it follows from Lemma VI.5.3 that for v > 0 the operator ( T — λ 。 I ) - ' is compact . Thus , if v > 0 , then ...
Page 2462
Nelson Dunford, Jacob T. Schwartz. = is compact . Put CQR1 , and D R2 , so that VCD . The operator C is compact by Corollary VI.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a compact operator in H , and ...
Nelson Dunford, Jacob T. Schwartz. = is compact . Put CQR1 , and D R2 , so that VCD . The operator C is compact by Corollary VI.5.5 , and thus proof of Corollary 11 is complete . Q.E.D. 12 LEMMA . If C is a compact operator in H , and ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
36 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 follows from Theorem 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