## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 81

Page 22

Since a

of only a

have a convergent subsequence. This contradiction proves that A is sequentially

...

Since a

**finite number**of these neighborhoods cover A, the sequence {a,} consistsof only a

**finite number**of distinct points of A, and therefore most certainly doeshave a convergent subsequence. This contradiction proves that A is sequentially

...

Page 200

P.), ote which has the following properties: S is the Cartesian product P.S.; ge.A 2

is the a-field determined by all subsets of S of the form E = P E, ae.A where E, e 2,

and, with a

P.), ote which has the following properties: S is the Cartesian product P.S.; ge.A 2

is the a-field determined by all subsets of S of the form E = P E, ae.A where E, e 2,

and, with a

**finite number**of exceptions, E. = S.; and Au is a measure on 2 with ...Page 579

If T is a compact operator, its spectrum is at most denumerable and has no point

of accumulation in the compler plane earcept possibly A = 0. Every non-zero

If T is a compact operator, its spectrum is at most denumerable and has no point

of accumulation in the compler plane earcept possibly A = 0. Every non-zero

**number**in g(T) is a pole of T and has**finite**positive indea. For such a**number**2, ...### What people are saying - Write a review

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

### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

### Other editions - View all

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero