Linear Operators: Spectral operators |
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Page 2025
... gives ( 40 ) | λ - √xy ( 8 ) | n 1 = | 4 ( 8 ) | ≤ M n = 1 , 2 , ... u ( m - X ) Since ( √ ( 8 ) ) > w we may fix À so large that | λ — Âμ¿ ( $ ) | < λ — w and thus the fraction appearing in ( 40 ) approaches zero as no . Q.E.D. It ...
... gives ( 40 ) | λ - √xy ( 8 ) | n 1 = | 4 ( 8 ) | ≤ M n = 1 , 2 , ... u ( m - X ) Since ( √ ( 8 ) ) > w we may fix À so large that | λ — Âμ¿ ( $ ) | < λ — w and thus the fraction appearing in ( 40 ) approaches zero as no . Q.E.D. It ...
Page 2031
... gives ( FT ̧ ) ( q ) = { _ _ ( Fq ) ( s ) 4 ( s ) ds = [ _ _p ( s ) ( F4 ) ( s ) ds RN RN Un = TFU ( P ) , ΚΕΦ . ( XI.1 ) and F is Now is dense in = L2 ( RN ) and thus there is for an arbitrary in Ha ≤ Ø n → H. FØ 5 a sequence { n } ...
... gives ( FT ̧ ) ( q ) = { _ _ ( Fq ) ( s ) 4 ( s ) ds = [ _ _p ( s ) ( F4 ) ( s ) ds RN RN Un = TFU ( P ) , ΚΕΦ . ( XI.1 ) and F is Now is dense in = L2 ( RN ) and thus there is for an arbitrary in Ha ≤ Ø n → H. FØ 5 a sequence { n } ...
Page 2065
... gives more by asserting that the inverse a1 is in A1 . 1 The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
... gives more by asserting that the inverse a1 is in A1 . 1 The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
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