## Linear Operators: Spectral theory |

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Page 855

Thus , for the reader who is familiar with the contents of

Thus , for the reader who is familiar with the contents of

**Chapters**I , II , III , and VII , there will be only occasional ...**Chapter**IX is an introduction to the much larger subject of B - algebras ; it serves us as a basis for the ...Page 887

**CHAPTER**X Bounded Normal Operators in Hilbert Space 1. Terminology and Preliminary Notions The spectral theorem to be proved in this**chapter**will introduce a theory which parallels in Hilbert space the theory in n - dimensional unitary ...Page 1185

**CHAPTER**XII Unbounded Operators in Hilbert Space 1. Introduction In the preceding**chapter**we have seen how the spectral theory developed in**Chapters**IX and X may be applied to various problems in mathematical analysis .### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero