Linear Operators: Spectral operators |
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Page 2092
... equivalent is indeed an equivalence relation and , when T and U are quasi - nilpotent equivalent , then ( i ) σ ( T ) = σ ( U ) , ( ii ) T has the single valued extension property if and only if U does , and ( iii ) if T ( hence U ) has ...
... equivalent is indeed an equivalence relation and , when T and U are quasi - nilpotent equivalent , then ( i ) σ ( T ) = σ ( U ) , ( ii ) T has the single valued extension property if and only if U does , and ( iii ) if T ( hence U ) has ...
Page 2105
... equivalent to | · | and relative to which all the operators E ( S ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒ ƒ ( 8 ) E ( ds ) || = sup | ƒ ( 8 ) ...
... equivalent to | · | and relative to which all the operators E ( S ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒ ƒ ( 8 ) E ( ds ) || = sup | ƒ ( 8 ) ...
Page 2115
... equivalent , then U is a spectral operator . Moreover , if T and U are spectral , then they are quasi - nilpotent equivalent if and only if they have the same resolution of the identity , and if and only if the single condition : lim ...
... equivalent , then U is a spectral operator . Moreover , if T and U are spectral , then they are quasi - nilpotent equivalent if and only if they have the same resolution of the identity , and if and only if the single condition : lim ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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