Linear Operators: Spectral operators |
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Page 1989
... measure in 5 , and thus , since F is unitary , the measure e ( σ ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e - almost ...
... measure in 5 , and thus , since F is unitary , the measure e ( σ ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e - almost ...
Page 2110
... measure into the space of con- tinuous operators in a space E in which closed bounded sets are compact ( for example , a Montel space ) , then μ is purely atomic . In Walsh [ 3 ] this was extended to the case where E has the property ...
... measure into the space of con- tinuous operators in a space E in which closed bounded sets are compact ( for example , a Montel space ) , then μ is purely atomic . In Walsh [ 3 ] this was extended to the case where E has the property ...
Page 2111
... measure of x . However , not every operator has a non - trivial T - measure ; consider the right shift operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes ...
... measure of x . However , not every operator has a non - trivial T - measure ; consider the right shift operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes ...
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