Linear Operators: Spectral operators |
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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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero