CONTENTS -- Preface -- Linearity in Non-Linear Situations R. M. Aron -- 1. Two introductions -- 2. Lineability of the zeros of polynomials -- 3. Non-spaceability of differentiable functions -- 4. Lineability of hypercyclic operators -- 5. Baire category and lineability -- References -- Alexander Grothendieck's Work on Functional Analysis F. Bombal -- 1. Introduction -- 2. Grothendieck and Functional Analysis -- 2.1. The Thesis: "Produits tensoriels topologiques et espaces nucle'aires. " -- 2.1.1. I.- The approximation property. -- 2.1.2. II.- Nuclear, integral and related operators. -- 2.1.3. III. The kernel theorem and nuclear spaces. -- 2.2. The Dunford-Pettis and relatives properties. -- 2.2.1. The Dunford-Pettis property. -- 2.2.2. The reciprocal Dunford Pettis and the Dieudonne' properties. -- 2.2.3. The "Grothendieclc spaces" and the hereditary properties. -- 2.3. The Sao Paulo's LLRe'sume''' -- 3. Conclusion -- Appendix A. Grothendieck's Publications on Functional Analysis. -- References -- The Hardy-Littlewood Maximal Function and Some of Its Variants J. Duoandikoetxea -- 1. Introduction -- 2. The one-dimensional maximal function -- 2.1. Strong and weak estimates -- 2.2. The differentiation theorem -- 3. The maximal function in higher dimensions -- 3.1. Directional maximal functions -- 4. The strong maximal function -- 5. The universal maximal function -- 6. Differentiation bases -- 7. Some further developments -- 8. The Kakeya maximal operator -- 8.1. The size conjecture -- 8.2. Bochner-Riesz multipliers -- 8.3. The dimension conjecture -- 8.4. Radial functions -- 9. Maximal operators on sets of directions -- 9.1. Finite sets of directions -- 9.2. Infinite sets of directions -- References -- Linear Dynamics G. Godefroy -- 1. HYPERCYCLIC OPERATORS -- 2. BAIRE CATEGORY TECHNIQUES -- 3. THE ROLE OF THE UNIMODULAR POINT SPECTRUM.

4. OPERATORS WITH PRESCRIBED ORBIT -- 5. THE MAIN PROBLEM -- References -- Greedy Algorithms and Bases from the Point of View of Banach Space Theory N. J. Kalton -- 1. Introduction -- 2. Greedy and quasi-greedy bases -- 3. Almost greedy bases and duality -- 4. Existence of quasi-greedy and almost greedy bases -- 5. Basic sequences: an open question -- 6. More general greedy algorithms -- References -- On the Hahn-Banach Theorem L. Narici -- 1. What is it? -- 2. The Obvious Solution -- 3. The Times -- 3.1. The Evolution of the FzLnction Concept -- Analysis on Spaces of Functions -- 3.2. Structure and Isomorphism -- 3.3. Spatial Imagery and the Euclidean Renaissance -- 4. Origins -- 4.1. Systems of Linear Equations -- 4.2. Riesz -- 4.3. The First Normed Space -- 4.4. Enter Helly -- 4.5. Hahn and Banach -- 5. The Complex Case -- 6. A Theorem for Linear Maps? (not Functionals) -- 6.1. Intersection Properties -- 6.2. Examples on Extendible Spaces -- 6.3. The Domain -- 6.4. Superspaces and Functionals -- 6.5. Superspaces and Linear Maps -- 7. Uniqueness of the Extension -- 7.1. Non- Uniqueness -- 7.2. Unique Extensions of the Same Norm: Special Cases -- 7.3. Uniqueness of Dominated Extensions -- 7.4. Unique Extensions for Points and Subspaces-Best Approximations from M -- 7.5. Unique Extensions for all Subspaces-Rotund Dual -- 8. Non- Archimedean Functional Analysis -- 9. The Axiom of Choice -- 9.1. Is HB AC? -- 9.2. Avoiding AC -- 10. "Sandwich Theorems" and Another Approach -- 11. Locally Convexity and Hahn-Banach Extensions -- References -- Spectral Properties of Cesbro-like Operators M. M. Neumann -- 1. Introduction and outline -- 2. Basic definitions and notation -- 3. The classical Cesho operator -- 4. Generalized Cesaro operators -- 5. The spectral picture -- 6. Subnormality and hyponormality -- 7. Subdecomposability.

8. The case of weighted Bergman spaces -- References -- Tribute to Miguel de Guzmh: Reflections on Matematical Education Centered on the Mathematical Analysis B. Rubio Segouia -- On Certain Spaces of Holomorphic Functions M. Valdiuia -- 1. Introduction and notation -- 2. Nearly-Baire spaces -- 3. The space ' H ( ) -- References -- Classical Potential Theory and Analytic Capacity J. Verdera -- 1. Introduction -- 2. Elementary Electrostatics -- 2.1. Coulomb's Law -- 2.2. The equilibrium potential -- 2.3. Energy -- 2.4. Energy as a quadratic forrn i n a Hilbert space -- 2.5. Capacity -- 2.6. Critical size of sets of zero capacity -- 2.7. Sub-additivity of capacity -- 3. Analytic capacity -- 3.1. Removable sets for bounded analytic functions -- 3.2. Old problems on analytic capacity -- 3.3. Some open problems -- Acknowledgments -- References -- Best Approximations on Small Regions - A General Approach F. Zd and H. H. Cuenya -- 1. Introduction -- 2. The norm set up -- 3. The Taylor polynomial and the limit of best approximat ion polynomials -- 4. The asymptotic behavior of the error -- 5. The limit of best approximation polynomials -- References.