## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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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

least two ...

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 I and if o(T) contains atleast two ...

Page 935

A somewhat stronger result has been proved by Singer and Wermer [1] who

obtained a theorem implying that if A and B are bounded

and if AB — BA lies in the uniformly closed algebra generated by A and I , then

AB ...

A somewhat stronger result has been proved by Singer and Wermer [1] who

obtained a theorem implying that if A and B are bounded

**operators**on a B-spaceand if AB — BA lies in the uniformly closed algebra generated by A and I , then

AB ...

Page 1016

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

operators. To show that this is indeed the case we need to derive a variety of ...

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

**linear****operator**in Hilbert space are irrevocably lost, will be retained by Hilbert-Schmidtoperators. To show that this is indeed the case we need to derive a variety of ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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