## Linear Operators: Spectral theory |

### From inside the book

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Page 930

It is not known whether every operator, distinct from the zero and identity

operators, has a non-trivial invariant subspace. It is readily seen from Theorem

VII.3.10 that if T is a bounded

at least ...

It is not known whether every operator, distinct from the zero and identity

operators, has a non-trivial invariant subspace. It is readily seen from Theorem

VII.3.10 that if T is a bounded

**linear operator**in a B-space 3; and if o(T) containsat least ...

Page 935

Every bounded

form UP where U is a partial isometry and P is a positive

then U may be taken to be unitary and such that U and P commute with each

other ...

Every bounded

**linear**transformation T in a Hilbert space can be written in theform UP where U is a partial isometry and P is a positive

**operator**. If T is normal,then U may be taken to be unitary and such that U and P commute with each

other ...

Page 1016

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. properties

of finite dimensional operators, which in the case of a general

Hilbert space are irrevocably lost, will be retained by Hilbert-Schmidt operators.

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. properties

of finite dimensional operators, which in the case of a general

**linear operator**inHilbert space are irrevocably lost, will be retained by Hilbert-Schmidt operators.

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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