## Linear Operators: General theory |

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Page 475

CHAPTER VI

linear maps between Bspaces begun in Chapter II . Various

introduced in the space B ( X , Y ) of bounded linear maps between the B -

spaces X and ...

CHAPTER VI

**Operators**and Their Adjoints This chapter continues the study oflinear maps between Bspaces begun in Chapter II . Various

**topologies**areintroduced in the space B ( X , Y ) of bounded linear maps between the B -

spaces X and ...

Page 477

strong , and the weak

uniform

the strong

...

strong , and the weak

**operator topologies**in B ( X , Y ) . It is evident that theuniform

**operator topology**is stronger than the strong**operator topology**, and thatthe strong

**operator topology**is stronger than the weak**operator topology**. With its...

Page 513

topology , but that { A , A * } does not converge to zero in this topology even

though { A * An } converges to zero in the strong

Hilbert space , the mapping T → T * of B ( H ) into itself is continuous with either

the ...

topology , but that { A , A * } does not converge to zero in this topology even

though { A * An } converges to zero in the strong

**operator topology**. 12 If H is aHilbert space , the mapping T → T * of B ( H ) into itself is continuous with either

the ...

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### Contents

Preliminary Concepts A Settheoretic Preliminaries 1 Notation and Elementary Notions | 1 |

Partially Ordered Systems | 7 |

Exercises | 9 |

Copyright | |

35 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

algebra analytic applied arbitrary assumed B-space ba(S Borel bounded called Chapter clear closed compact complex condition Consequently constant contains continuous functions converges Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hausdorff Hence Hilbert space identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear space mapping Math means measure space neighborhood norm obtained operator positive measure preceding projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero