## Linear Operators: Spectral theory |

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Page 1809

1. On dominated ergodic theorems in L, ... On B+-algebras.

321–327 (1951). 3. On a theorem of Gelfand and Neumark and the B"-algebra.

**Proc**. Nat. Acad. Sci. U.S.A. 36, 35–40 (1950). Fukamiya, M. (see also Yosida, K.)1. On dominated ergodic theorems in L, ... On B+-algebras.

**Proc**. Japan Acad. 27,321–327 (1951). 3. On a theorem of Gelfand and Neumark and the B"-algebra.

Page 1845

on Banach spaces (IV). On a decomposition of additive set functions.

Acad. Tokyo 18, 333-335 (1942). Nakamura, M., and Umegaki, H. 1. A remark on

...

**Proc**. Japan Acad. 27, 544–547 (1951). Nakamura, M., and Sunouchi, S. 1. oteon Banach spaces (IV). On a decomposition of additive set functions.

**Proc**. Imp.Acad. Tokyo 18, 333-335 (1942). Nakamura, M., and Umegaki, H. 1. A remark on

...

Page 1879

functions.

equivalence in general Euclidean space.

4.

**Proc**. Imp. Acad. Tokyo 17, 121–124 (1941). 2. Vector lattices and additive setfunctions.

**Proc**. Imp. Acad. Tokyo 17, 228–232 (1941). 3. On the unitaryequivalence in general Euclidean space.

**Proc**. Japan Acad. 22, 242–245 (1946).4.

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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