## Linear Operators: General theory |

### From inside the book

Results 1-3 of 63

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 x...

Page 246

Thus the

the

3.19), the

...

Thus the

**dimension**of X* is n. Conversely, let the**dimension**of X* be**finite**. Thenthe

**dimension**of X** is**finite**, and. since X is equivalent to a subspaee of X** (II.3.19), the

**dimension**of X is**finite**. Hence, from the first part of this proof, X and X*...

Page 556

Spectral Theory in a

denote a

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

Spectral Theory in a

**Finite Dimensional**Space Throughout this section, 3£ willdenote a

**finite dimensional**complex fi-space, and T a linear operator in B(£). Ouraim is to study the algebraic and topological properties of T. This is achieved, ...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

79 other sections not shown

### Other editions - View all

### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional 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 Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact