## Linear Operators: General theory |

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Page 243

The norm in is |ixr J = (x, x)112. 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

The norm in is |ixr J = (x, x)112. 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 nortned linear spaces is used as a normed space,

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

are

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

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

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 | |

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a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero