Linear Operators: Spectral operators |
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Page 1951
... belong to the right ( left ) ideal J in B ( X ) . Then every projection E ( o ) with 0 ₫ ō belongs to J. If I is closed , then S and N also belong to J. PROOF . Let 0 σ and let T , = TE ( o ) | E ( o ) X , the restriction of T to the ...
... belong to the right ( left ) ideal J in B ( X ) . Then every projection E ( o ) with 0 ₫ ō belongs to J. If I is closed , then S and N also belong to J. PROOF . Let 0 σ and let T , = TE ( o ) | E ( o ) X , the restriction of T to the ...
Page 2263
... belongs to the continuous spectrum of the spectral operator S. The point vo belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. PROOF . It follows from Lemma 19 ...
... belongs to the continuous spectrum of the spectral operator S. The point vo belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. PROOF . It follows from Lemma 19 ...
Page 2462
... belongs to the trace class . Then , by what we have already proved , T , A converges to zero in norm , and thus , by Lemma XI.9.9 , TC = ( TA ) B converges to zero in trace norm . By Lemma XI.9.6 ( c ) and Definition XI.9.1 , C * belongs ...
... belongs to the trace class . Then , by what we have already proved , T , A converges to zero in norm , and thus , by Lemma XI.9.9 , TC = ( TA ) B converges to zero in trace norm . By Lemma XI.9.6 ( c ) and Definition XI.9.1 , C * belongs ...
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