## Linear Operators: General theory |

### From inside the book

Results 1-3 of 37

Page 577

Since by

that E(X)x = x. This proves that {x\(T—?J)'x = 0} Q 3ŁA which, when combined

with (ii), completes the proof of the

Compact ...

Since by

**Theorem**20, (T— XI) is one-to-one on it follows that E{a1)x = 0 and thusthat E(X)x = x. This proves that {x\(T—?J)'x = 0} Q 3ŁA which, when combined

with (ii), completes the proof of the

**theorem**. Q.E.D. 4.**Spectral**Theory ofCompact ...

Page 609

oped the ideal theory of jB-algebras. In addition, Gelfand used the contour

integral to obtain idempotents in B-algebras. Independently, Lorch [6] employed

the same device and initiated a study of "

[1].

oped the ideal theory of jB-algebras. In addition, Gelfand used the contour

integral to obtain idempotents in B-algebras. Independently, Lorch [6] employed

the same device and initiated a study of "

**spectral Theorem**8.10 is due to Gelfand[1].

Page 750

18.

D. S. 1. On the ergodic

**Spectral**tlieory. II. Resolutions of the identity. Pacific J. Math. 2, 559-614 (1952).18.

**Spectral**operators. Pacific J. Math. 4, 321-354 (1954). Dunford, N., and Miller,D. S. 1. On the ergodic

**theorem**. Trans. Amer. Math. Soc. 60, 538-549 (1946).### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

79 other sections not shown

### Other editions - View all

### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero