Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 87
Page 2308
... Theorem XIII.2.10 and by Lemma XII.1.6 ( a ) , it follows from Definition XIII.2.17 and the remark preceding Definition XIII.2.29 , that S is closed . From this , it follows immediately that S - XI is closed , and hence from Lemma XII ...
... Theorem XIII.2.10 and by Lemma XII.1.6 ( a ) , it follows from Definition XIII.2.17 and the remark preceding Definition XIII.2.29 , that S is closed . From this , it follows immediately that S - XI is closed , and hence from Lemma XII ...
Page 2364
... Lemma 2.2 , it follows from Lemma VII.6.6 and Theorem VI.5.4 that K ( n ) is a compact operator which depends analytically on n for | n | < 1 + d1 . It follows from Lemma VII.6.6 that if O is any bounded open set whose boundary does not ...
... Lemma 2.2 , it follows from Lemma VII.6.6 and Theorem VI.5.4 that K ( n ) is a compact operator which depends analytically on n for | n | < 1 + d1 . It follows from Lemma VII.6.6 that if O is any bounded open set whose boundary does not ...
Page 2479
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to 5 of the operator H of Lemma 15 ( cf. ( 33 ) ... follows by Lemma 13 that , if is sufficiently large , we have ( 83 ) - 1 ( λ 。 I — H1 ) − 1 — ( λ 。 I — H ) − 1 ...
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to 5 of the operator H of Lemma 15 ( cf. ( 33 ) ... follows by Lemma 13 that , if is sufficiently large , we have ( 83 ) - 1 ( λ 。 I — H1 ) − 1 — ( λ 。 I — H ) − 1 ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
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