## Linear Operators: Spectral theory |

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Page 906

A bounded operator T in Hilbert space X is called

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

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

for ...

A bounded operator T in Hilbert space X 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 (Tr, ar) > 0 for every a in S); and positive definite if it is positive and (Tw, w) > 0

for ...

Page 1146

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

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

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

Page 1148

Moreover, H is the direct sum of a finite number of groups H, each of which is

either (1) The additive group of the real axis; or (2) The group SU(n) of all n x n

complex

...

Moreover, H is the direct sum of a finite number of groups H, each of which is

either (1) The additive group of the real axis; or (2) The group SU(n) of all n x n

complex

**unitary**matrices of determinant 1; or (3) The group SpU(n) of all 2n × 2n...

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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