## Linear Operators, Part 1 |

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Page 243

The function (-, -) is called the scalar or inner product in S) and (r, y) is called the

scalar or inner product of a and y. The norm in S) is a = (v, w)”. Remark.

...

The function (-, -) is called the scalar or inner product in S) and (r, y) is called the

scalar or inner product of a and y. The norm in S) is a = (v, w)”. 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 3:1, ..., *, 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 3:1, ..., *, are

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

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero