## 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 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero