## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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this is far from clear , and it is of considerable interest to find non - trivial invariant subspaces for a given

this is far from clear , and it is of considerable interest to find non - trivial invariant subspaces for a given

**operator**. It is not known whether every**operator**, distinct from the zero and identity operators , has a non - trivial ...Page 1200

If T is a self

If T is a self

**adjoint operator**and if f is the polynomial | ( 2 ) = co + = 40 + ... + m2m then the operator f ( T ) of Definition 5 is the same as the operator ( T ) of Definition VII.9.6 . This operator f ( T ) is also the same as the ...Page 1223

Consider , as an example , an

Consider , as an example , an

**operator**which will be studied in greater detail in the next chapter : the differential**operator**iD = i ( d / dt ) ... This choice of domain will make the**operator**iD symmetric , but still not self**adjoint**.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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