## Linear Operators: Spectral theory |

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Page 1801

69, 276-291 (1950). Operations in

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.

69, 276-291 (1950). 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.

Page 1845

(Spanish. French summary). 2. A characterization of the normed vector ordered

705 (1949). 3. A theorem of the Hahn-

Trans.

(Spanish. French summary). 2. A characterization of the normed vector ordered

**spaces**of continuous functions over a compact**space**. Amer. J. Math. 71, 701–705 (1949). 3. A theorem of the Hahn-

**Banach**type for linear transformations.Trans.

Page 1858

Perturbations of linear operators in

fields of scalars in Hilbert space. Acta Math ... On the Fredholm theory of integral

equations for operators belonging to the trace class of a general

Perturbations of linear operators in

**Banach spaces**. ... Critical points and gradientfields of scalars in Hilbert space. Acta Math ... On the Fredholm theory of integral

equations for operators belonging to the trace class of a general

**Banach space**.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

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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