## Linear Operators: General theory |

### From inside the book

Results 1-3 of 30

Page 36

7 that in every linear vector space X there is a maximal linearly

. A subset B of the linear space X is called a Hamel basis or a Hamel base for X if

every vector x in X has a unique representation x = Qzba t . . . tambn with di € 0 ...

7 that in every linear vector space X there is a maximal linearly

**independent**set B. A subset B of the linear space X is called a Hamel basis or a Hamel base for X if

every vector x in X has a unique representation x = Qzba t . . . tambn with di € 0 ...

Page 252

converges and is

arranged . The operator E is the orthogonal projection on the closed linear

manifold determined by A . Proof . Let Yı , . . . , Yn be distinct elements of A and let

y = X - 1 ...

converges and is

**independent**of the order in which its non - zero terms arearranged . The operator E is the orthogonal projection on the closed linear

manifold determined by A . Proof . Let Yı , . . . , Yn be distinct elements of A and let

y = X - 1 ...

Page 697

7 ( 4 , . . . , tx ) dt . . . dtxe Then there is an absolute constant Ck , which is

s ) lu ( ds ) , B > 0 , - CkB I el caß ) where e * ( B ) = { s \ * ( s ) > B } and elß ) = { s \

\ \ ( s ) ...

7 ( 4 , . . . , tx ) dt . . . dtxe Then there is an absolute constant Ck , which is

**independent**of the semigroup and**independent**of f , such that u ( e * ( P ) ) S . 1 (s ) lu ( ds ) , B > 0 , - CkB I el caß ) where e * ( B ) = { s \ * ( s ) > B } and elß ) = { s \

\ \ ( s ) ...

### 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 | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero