Linear Operators: Spectral operators |
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Page 2232
... Q is closed . Let { n } be a second increasing sequence of elements of 。 such that E ( U = 1 ) = I , and let Q be defined by the equations D ( Q ) = { x lim QoE ( e ) x exists } , Qx - lim QoE ( en ) x , x = D ( Q ) . 818 To complete ...
... Q is closed . Let { n } be a second increasing sequence of elements of 。 such that E ( U = 1 ) = I , and let Q be defined by the equations D ( Q ) = { x lim QoE ( e ) x exists } , Qx - lim QoE ( en ) x , x = D ( Q ) . 818 To complete ...
Page 2250
... let q = { f ( ∞ ) } ; if ƒ is not analytic at infinity , let q be the null set . Let q ' be the open set U - q . The conclusion of the theorem will be divided into two parts . ( a ) ( b ) g ( f ( T ) ) | E1 ( q ) X = h ( T ) | E1 ( q ) ...
... let q = { f ( ∞ ) } ; if ƒ is not analytic at infinity , let q be the null set . Let q ' be the open set U - q . The conclusion of the theorem will be divided into two parts . ( a ) ( b ) g ( f ( T ) ) | E1 ( q ) X = h ( T ) | E1 ( q ) ...
Page 2415
... q ( A1 ) given by Theorem 8 , then since T , and T are similar , ( AIT ) -1 exists and is everywhere defined and ... Let be a complex B - space . Let D be a subdomain of the complex plane which is not dense in the complex plane . Let 1 ...
... q ( A1 ) given by Theorem 8 , then since T , and T are similar , ( AIT ) -1 exists and is everywhere defined and ... Let be a complex B - space . Let D be a subdomain of the complex plane which is not dense in the complex plane . Let 1 ...
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