## Advanced Courses of Mathematical Analysis IV: Proceedings of the Fourth International School - In Memory of Professor Antonio Aizpuru TomasF. Javier Perez-Fernandez, Fernando Rambla-Barreno This proceedings is a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory. The works are a fundamental source for current and future developments in these research fields. The articles and surveys have been collected as well as reference results scattered in the corresponding literature and thus, are highly useful to researchers. |

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### Contents

Professor Antonio Aizpuru F Javier P erezFern andez | 1 |

Part A Minicourses | 11 |

Part B Plenary speakers | 143 |

Author Index | 247 |

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### Common terms and phrases

ˇSemrl a-polaroid additive map admits an isometric Aiena Anal Antonio Aizpuru approximation property Aron Aus(B Banach algebras Banach operator ideal Banach space baſ.A bilinear bounded linear operators bounded operator Browder's theorem closed compact continuous convergence Corollary countably additive defined Definition denote dual exists Fredholm Fredholm operators functions Garc´ıa Garc´ıa-Pacheco Hausdorff space hence Hilbert space homomorphism inequality integer isolated point isometric shift Jordan homomorphism left polaroid Lemma lineability linear map Linear maps preserving Lip(X Mathematics non-negative norm Outer measure pairwise disjoint polaroid polaroid operators polynomials problem Proof Proposition result Riesz basis satisfies semi-Fredholm operators Seoane-Sepúlveda ſº spectral spectrum Studia Math subsets subspace Suppose surjective SVEP symmetric tensor Theorem 3.1 theorem holds uniformly unit ball vector Weyl type theorems Weyl’s theorem