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

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Page 879

14 DEFINITION . A bounded

normal if TT * = T * T , and self adjoint if T = T * . It is clear that the smallest closed

subalgebra of B ( H ) which contains a normal operator T , its adjoint T * , and the

...

14 DEFINITION . A bounded

**linear operator**T in a Hilbert space is said to benormal if TT * = T * T , and self adjoint if T = T * . It is clear that the smallest closed

subalgebra of B ( H ) which contains a normal operator T , its adjoint T * , and the

...

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

contains at ...

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 X and if o ( T )contains at ...

Page 1273

If T is a

numbers a such that the inverse operator ( T - 21 ) -1 exists and is bounded on its

domain . The set y ( T ) is called the domain of regularity of T ( or the set of points

of ...

If T is a

**linear operator**with dense domain , let y ( T ) be the set of all complexnumbers a such that the inverse operator ( T - 21 ) -1 exists and is bounded on its

domain . The set y ( T ) is called the domain of regularity of T ( or the set of points

of ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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