## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2291

A number of results concerning the conditional convergence of eigenvalue

expansions are mentioned in Section 6 below . 2 . The Principal Abstract

whose ...

A number of results concerning the conditional convergence of eigenvalue

expansions are mentioned in Section 6 below . 2 . The Principal Abstract

**Perturbation**Theorem In this section we shall study**perturbations**of an operatorwhose ...

Page 2530

Amer . Math . Soc . , Providence , R . I . , 1965 . 18 . Spectral

phenomena .

Wiley , New ...

**Perturbation**of spectra in Hilbert space . Lectures in Applied Math . , Vol . III ,Amer . Math . Soc . , Providence , R . I . , 1965 . 18 . Spectral

**perturbation**phenomena .

**Perturbation**Theory and its Applications in Quantum Mechanics ,Wiley , New ...

Page 2546

Soc . Japan 11 , 246 – 262 ( 1959 ) . II . ibid . 12 , 243 – 257 ( 1960 ) . 4 . On a

generalization of the Weinstein - Aronszajn formula and the infinite determinant .

Sci .

**Perturbation**of continuous spectra by unbounded operators , I , II . I . J . Math .Soc . Japan 11 , 246 – 262 ( 1959 ) . II . ibid . 12 , 243 – 257 ( 1960 ) . 4 . On a

generalization of the Weinstein - Aronszajn formula and the infinite determinant .

Sci .

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero