## Linear Operators: General theory |

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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 ... If T is a

it is said to be a

TT ...

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 ... If T is a

**linear operator**on X to X ,it is said to be a

**linear operator**in X . For such operators the symbol T2 is used forTT ...

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 ...

Page 838

8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a

orthogonal and orthonormal bases in ... 8 ( 223 ) Borel - Stieltjes measure , ( 142

) Bound , of an

the ...

8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a

**linear**space . ( See Hamel base )orthogonal and orthonormal bases in ... 8 ( 223 ) Borel - Stieltjes measure , ( 142

) Bound , of an

**operator**, II . 3 . 5 ( 60 ) in a partially ordered set , I . 2 . 3 ( 4 ) inthe ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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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