## Linear Operators, Part 1 |

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Page 243

... norm in H is x1 = ( x , x ) 1/2 Remark .

of abstract axioms . It is noteworthy that some of the concrete spaces defined

above satisfy these axioms , and hence are special cases of abstract

... norm in H is x1 = ( x , x ) 1/2 Remark .

**Hilbert space**has been defined by a setof abstract axioms . It is noteworthy that some of the concrete spaces defined

above satisfy these axioms , and hence are special cases of abstract

**Hilbert****space**.Page 247

closely related , especially in its elementary geometrical aspects , to the

Euclidean or finite dimensional unitary spaces . It is not immediate from the

definition ( 2.26 ) ...

**Hilbert Space**Of the infinite dimensional B - spaces ,**Hilbert space**is the mostclosely related , especially in its elementary geometrical aspects , to the

Euclidean or finite dimensional unitary spaces . It is not immediate from the

definition ( 2.26 ) ...

Page 256

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X , ... , Xn

are

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X , ... , Xn

are

**Hilbert spaces**then it will always be understood , sometimes without explicit ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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