Linear Operators: Spectral operators |
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Page 2312
... space X. Let f * , f * , ... , f * be a basis for the solutions of the equation ( T * −λ 。) ƒ * = 0 and let Σ be ... Banach space . It is well to remark , how- ever , that in the special case in which the Banach space is Hilbert space ...
... space X. Let f * , f * , ... , f * be a basis for the solutions of the equation ( T * −λ 。) ƒ * = 0 and let Σ be ... Banach space . It is well to remark , how- ever , that in the special case in which the Banach space is Hilbert space ...
Page 2313
... Banach space adjoint , contrary to our practice in other Banach spaces . This has the effect of introducing complex conjugates in many of the Hilbert - space formulas where the corresponding Banach - space formulas do not have complex ...
... Banach space adjoint , contrary to our practice in other Banach spaces . This has the effect of introducing complex conjugates in many of the Hilbert - space formulas where the corresponding Banach - space formulas do not have complex ...
Page 2541
... space . Trans . Amer . Math . Soc . 113 , 488-511 ( 1964 ) . Kaniel , S ... Banach algebras for algebra - valued functions . Trans . Amer . Math . Soc ... Banach space . Bull . Amer . Math . Soc . 71 , 891-893 ( 1965 ) . A Jordan ...
... space . Trans . Amer . Math . Soc . 113 , 488-511 ( 1964 ) . Kaniel , S ... Banach algebras for algebra - valued functions . Trans . Amer . Math . Soc ... Banach space . Bull . Amer . Math . Soc . 71 , 891-893 ( 1965 ) . A Jordan ...
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