## Linear Operator Theory in Engineering and ScienceThis book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook. |

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### Contents

Introduction | 1 |

SetTheoretic Structure | 11 |

Topological Structure | 43 |

Introduction to Metric Spaces | 45 |

Some Deeper Metric Space Concepts | 77 |

Algebraic Structure | 159 |

Introduction to Linear Spaces | 161 |

Further Topics | 196 |

Banach Spaces | 215 |

Hilbert Spaces | 272 |

Special Operators | 352 |

Analysis of Linear Operators Compact Case | 395 |

An Illustrative Example | 397 |

The Spectrum | 411 |

Spectral Analysis | 439 |

Analysis of Unbounded Operators | 485 |

### Common terms and phrases

adjoint algebraic arbitrary assume Banach space bounded linear operator Cauchy sequence closed linear subspace closed set compact operators complete complex numbers concept consider Continuation of Exercise continuous functions continuous linear convergent sequence COROLLARY countable definition denote the collection dense differential eigenvalues eigenvectors equation equivalent EXAMPLE exists Figure finite finite-dimensional functions defined given Hamel basis Hence Hilbert space Hint homeomorphism Inequality infinite inner product space input interval inverse Lebesgue integral Lemma linear functional linear mapping linear subspace linear transformation linearly independent matrix metric space X,d neighborhood nonempty nonzero normed linear space one-to-one open set orthogonal projection orthonormal basis orthonormal set Proof random variables reader real numbers satisfies Section self-adjoint operator sequentially compact solution space H spectrum structure subset sum of projections symmetric operator topological totally bounded unique usual metric vector weighted sum x e H