## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 65

Page 1801

Operations in

Ergodic theorems for abelian semi-groups. Trans. Amer. Math. Soc. 51, 399-412 (

1942). Strict convexity and smoothness of normed spaces. Trans. Amer. Math.

Soc.

Operations in

**Banach**spaces. Trans.Amer. Math. Soc. 51, 583-608 (1942).Ergodic theorems for abelian semi-groups. Trans. Amer. Math. Soc. 51, 399-412 (

1942). Strict convexity and smoothness of normed spaces. Trans. Amer. Math.

Soc.

Page 1856

The singular elements of a

. 5. Isomorphic groups of linear transformations. Amer. J. Math. 72,451–464 (

1950). 6.

550 ...

The singular elements of a

**Banach**algebra. Duke Math. J. 14, 1063–1077 (1947). 5. Isomorphic groups of linear transformations. Amer. J. Math. 72,451–464 (

1950). 6.

**Banach**algebras with an adjoint operation. Ann. of Math. (2) 47, 528–550 ...

Page 1858

Elements of mathematical logic. Dover Publications, New York, 1950. 2.

Perturbations of linear operators in

. Rosenthal, A. (see Hahn, H., and Hartogs, F.) Rosser, J. B. 1. Logic for

mathematicians.

Elements of mathematical logic. Dover Publications, New York, 1950. 2.

Perturbations of linear operators in

**Banach**spaces. Arch. Math. 6, 89–101 (1955). Rosenthal, A. (see Hahn, H., and Hartogs, F.) Rosser, J. B. 1. Logic for

mathematicians.

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

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