Linear Operators: Spectral operators |
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Page 2022
... measurable function defined on the spec- trum σ ( A ̧ ) = σ ( Â ) . We simply define the p × p matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) = ƒ ( Â ( 8 ) ) . ( If the roots of the ...
... measurable function defined on the spec- trum σ ( A ̧ ) = σ ( Â ) . We simply define the p × p matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) = ƒ ( Â ( 8 ) ) . ( If the roots of the ...
Page 2404
... measurable function . For each number p such that 1 -1 1≤ p ≤∞ , define p ' by ( p ' ) − 1 + p ̄1 = 1. Put S S | A ( s , t ) \ " " μ ( dt ) } ° ' ° μ ( ds ) } " , 2 { p < 00 , ( 7 ) { A = D and ( 8 ) Moreover , in the extreme cases ...
... measurable function . For each number p such that 1 -1 1≤ p ≤∞ , define p ' by ( p ' ) − 1 + p ̄1 = 1. Put S S | A ( s , t ) \ " " μ ( dt ) } ° ' ° μ ( ds ) } " , 2 { p < 00 , ( 7 ) { A = D and ( 8 ) Moreover , in the extreme cases ...
Page 2410
... measurable function defined in D x D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) | A " ' = sup | A ( z , z ′ ) | < ∞ , 2.2 ED and let ( 4 ) be the integral operator defined by the equation ( 36 ) ...
... measurable function defined in D x D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) | A " ' = sup | A ( z , z ′ ) | < ∞ , 2.2 ED and let ( 4 ) be the integral operator defined by the equation ( 36 ) ...
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