## Linear Operators: General theory |

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Page 245

An n-dimensional B-space is equivalent to E". 4 Corollary. Every linear operator

on a

be a Hamel basis for the

...

An n-dimensional B-space is equivalent to E". 4 Corollary. Every linear operator

on a

**finite dimensional**normed linear space is continuous. Proof. Let {bv . . ., bn)be a Hamel basis for the

**finite dimensional**normed linear space X so that every a...

Page 246

Then the dimension of X** is finite, and, since X is equivalent to a subspace of X

** (II.8.19), the dimension of X is finite. ... 2<=ia;**(^*)''r- Q.E.D. From Corollary 7 it

follows that weak and strong convergence are the same in

Then the dimension of X** is finite, and, since X is equivalent to a subspace of X

** (II.8.19), the dimension of X is finite. ... 2<=ia;**(^*)''r- Q.E.D. From Corollary 7 it

follows that weak and strong convergence are the same in

**finite dimensional**...Page 556

Spectral Theory in a

denote a

Our aim is to study the algebraic and topological properties of T. This is achieved,

...

Spectral Theory in a

**Finite Dimensional**Space Throughout this section, £ willdenote a

**finite dimensional**complex JB-space, and T a linear operator in JB(X).Our aim is to study the algebraic and topological properties of T. This is achieved,

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

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a-finite 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 continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space 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 valued function vector space weak topology weakly compact weakly sequentially compact zero