Linear Operators: Spectral operators |
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Page 1930
... field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ( S ) T = TE ( S ) , σ ( T¿ ) ≤ 8 , δε Σ . δ Here we have used , and shall ...
... field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ( S ) T = TE ( S ) , σ ( T¿ ) ≤ 8 , δε Σ . δ Here we have used , and shall ...
Page 2143
... field ( T ) is not necessarily a σ - field , it is natural to ask whether or not the spectral measure E may be extended to the o - field generated by ( T ) . The following definition and theorems are concerned . with this question . 12 ...
... field ( T ) is not necessarily a σ - field , it is natural to ask whether or not the spectral measure E may be extended to the o - field generated by ( T ) . The following definition and theorems are concerned . with this question . 12 ...
Page 2145
... field other than the field of Borel sets . Such operators are described as follows . 1 DEFINITION . Let Σ be a field of sets in the complex plane and let T be a linear operator in the complex B - space X. Then a spectral measure E on Σ ...
... field other than the field of Borel sets . Such operators are described as follows . 1 DEFINITION . Let Σ be a field of sets in the complex plane and let T be a linear operator in the complex B - space X. Then a spectral measure E on Σ ...
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