## Linear Operators: General theory |

### From inside the book

Results 1-3 of 71

Page 37

If T : X + Y and U : Y → Z are linear transformations , and X , Y , Z are linear

spaces over the same field Ø , the product UT , defined by ( UT ) X = U ( Tx ) , is a

linear transformation which maps X into 3 . If T is a

said ...

If T : X + Y and U : Y → Z are linear transformations , and X , Y , Z are linear

spaces over the same field Ø , the product UT , defined by ( UT ) X = U ( Tx ) , is a

linear transformation which maps X into 3 . If T is a

**linear operator**on X to X , it issaid ...

Page 486

Linear combinations of compact

product of a compact

Linear combinations of compact

**linear operators**are compact operators , and anyproduct of a compact

**linear operator**and a bounded**linear operator**is a compact**linear operator**. PROOF . The conclusions of Theorem 4 follow readily from the ...Page 494

It is clear that the operator T , defined by ( b ) , is a bounded

S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T *

maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) ,

and ...

It is clear that the operator T , defined by ( b ) , is a bounded

**linear operator**on C (S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T *

maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) ,

and ...

### 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 | |

80 other sections not shown

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero