## Linear Operators: General theory |

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Page 253

For an orthonormal set ACQ the following statements are equivalent: (i) the set A

is complete; (ii) the set A is an orthonormal basis for !q; (iii) |af = EttA \(x, y)\\ X€§.

... That either one of these implies (iii)

For an orthonormal set ACQ the following statements are equivalent: (i) the set A

is complete; (ii) the set A is an orthonormal basis for !q; (iii) |af = EttA \(x, y)\\ X€§.

... That either one of these implies (iii)

**follows from Theorem**10 and Lemma 9.Page 557

Then P(T)!/ = P(A0)y, and, since P(T) = 0, it follows that P(A0) = 0. To prove that 0

^ 2? v^), we ... The

results for polynomial functions. 5 Theorem. If /, g are in 1F(T) and a, VII. 1.4 557 ...

Then P(T)!/ = P(A0)y, and, since P(T) = 0, it follows that P(A0) = 0. To prove that 0

^ 2? v^), we ... The

**following theorem**follows immediately from the correspondingresults for polynomial functions. 5 Theorem. If /, g are in 1F(T) and a, VII. 1.4 557 ...

Page 576

It

that it is an isomorphism, it will suffice to show that E(a) = 0 only when a is the

void set <f>. Now if E(a) = 0, then 3Ea = {0} and a(Ta) = <f>. It

It

**follows from Theorem**10 that the map a -> E(a) is a homeomorphism. To verifythat it is an isomorphism, it will suffice to show that E(a) = 0 only when a is the

void set <f>. Now if E(a) = 0, then 3Ea = {0} and a(Ta) = <f>. It

**follows from****Theorem**...### 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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