## Linear Operators: Spectral theory |

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Page 906

A bounded operator T in Hilbert space $) is called

called self adjoint, symmetric or Hermitian if T = To; positive if it is self adjoint and

if (Tw, w) > 0 for every a in Y); and positive definite if it is positive and (Tw, w) > 0

for ...

A bounded operator T in Hilbert space $) is called

**unitary**if TT* = To T = I; it iscalled self adjoint, symmetric or Hermitian if T = To; positive if it is self adjoint and

if (Tw, w) > 0 for every a in Y); and positive definite if it is positive and (Tw, w) > 0

for ...

Page 931

Applications are made to the restrictions of normal and

, Lumer, and Schäffer [1] proved that the restriction of a normal operator may

possess an inverse but not a square root (see also Halmos and Lumer [1]).

Dilations ...

Applications are made to the restrictions of normal and

**unitary**operators. Halmos, Lumer, and Schäffer [1] proved that the restriction of a normal operator may

possess an inverse but not a square root (see also Halmos and Lumer [1]).

Dilations ...

Page 1146

The following theorem is easily proved by induction in case R is

follows in the general case by the theorem stated above. THEoREM. Any finite

dimensional representation of a compact group G is a direct sum of irreducible ...

The following theorem is easily proved by induction in case R is

**unitary**, and thusfollows in the general case by the theorem stated above. THEoREM. Any finite

dimensional representation of a compact group G is a direct sum of irreducible ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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