## Linear Operators: General theory |

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Page 243

The function (•, •) is called the scalar or inner product in § and (x, y) is called the

scalar or inner product of x and y. The norm in § is |x] = (x, aj)1'2. Remark.

...

The function (•, •) is called the scalar or inner product in § and (x, y) is called the

scalar or inner product of x and y. The norm in § is |x] = (x, aj)1'2. Remark.

**Hilbert****space**has been -defined by a set of abstract axioms. It is noteworthy that some of...

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 #j. . . ., 3£„

arc

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 #j. . . ., 3£„

arc

**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 84 | 34 |

Copyright | |

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### Common terms and phrases

Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero