Descriptive Topology And Functional Analysis Ii: In Honour Of Manuel López-pellicer Mathematical Work, Elche, Spain, June 7-8, 2018 (springer Proceedings In Mathematics & Statistics)

This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel López-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas. Preface......Page 7 Contents......Page 8 Editor and Contributors......Page 10 1 Ph.D. Dissertation and Early Work......Page 13 2 Research on General Topology......Page 14 3.1 Strong Barrelledness Conditions......Page 15 3.2 On the Nikodým Boundedness Theorem......Page 18 3.3 Barrelled Spaces of Vector-Valued Functions......Page 20 3.4 Metrizability of Precompact Sets......Page 21 3.5 Closed Graph Theorems......Page 22 4.1 Bounding Tightness......Page 23 4.2 Bounded Tightness......Page 24 4.3 Trans-separable Spaces......Page 25 5.1 Tightness and Distinguished Fréchet Spaces......Page 27 5.2 Two Counterexamples......Page 28 5.3 Metrizable-Like Topological Groups......Page 29 5.4 ellc-Invariance of Some Topological Properties......Page 30 5.5 Rainwater Sets and Weak K-Analyticity of Cb( X)......Page 31 5.6 Quantitative Descriptive Topology......Page 32 7 Work as Editor-in-Chief of RACSAM......Page 34 References......Page 35 A Note on Nonautonomous Discrete Dynamical Systems......Page 40 1 Introduction......Page 41 2 Periodic Points......Page 42 3 Transitivity and NDS......Page 47 References......Page 51 Linear Operators on the (LB)-Sequence Spaces ces(p-), 1< p leqinfty......Page 53 1 Introduction......Page 54 2 The Space ces(p-)......Page 58 3 The Cesàro Operator on ces(p-)......Page 61 4 Multipliers on ces(p-)......Page 66 5 Operators from ces(p-) into ces(q-)......Page 70 6 Riesz Space Properties of ellp- and ces(p-)......Page 73 References......Page 76 1 Introduction......Page 78 2 Main Results......Page 80 References......Page 85 On Ultrabarrelled Spaces, their Group Analogs and Baire Spaces......Page 86 1 Main Results......Page 87 2 The Proofs......Page 91 References......Page 95 1 Introduction......Page 97 2.1 Pontryagin-van Kampen Duality......Page 99 3 Order Controllable Groups......Page 101 4 Group Codes......Page 103 References......Page 108 1 Introduction......Page 110 2 Preliminary Results......Page 113 3 General Results......Page 120 4 Real Locally Convex Spaces and Respecting Properties......Page 126 5 mathcalP-Barrelledness, Reflexivity and Respecting Properties......Page 131 6 Glicksberg Type Properties and the Property of Being a Mackey Group......Page 137 References......Page 141 1 Introduction......Page 144 2 KM-Fuzzy Metric Spaces......Page 146 3 Fuzzy Metric Spaces (in the Sense of George and Veeramani)......Page 147 4.1 Topology in a Fuzzy Metric Space......Page 148 4.2 Uniformity in Fuzzy Metric Spaces......Page 149 5 Completion of Fuzzy Metric Spaces......Page 150 6 Fuzzy Banach Contraction Principle in KM-Fuzzy Metric Spaces......Page 153 7 Fuzzy Banach Contraction Principle in Fuzzy Metric Spaces......Page 154 References......Page 156 1 Introduction......Page 159 1.2 Some Generalities on Norming Subspaces......Page 161 2 Property calP......Page 165 3.1 Compact Spaces and Properties calP and (M)......Page 169 3.2 Property calP, Corson and Valdivia Compacta......Page 171 3.3 Plichko Spaces with Property calP......Page 176 3.4 Properties calP and Mazur's......Page 177 References......Page 178 1 Introduction......Page 181 2 First Motivations and the Case Cp(βmathbbN)......Page 183 3 Proof of Theorem 2.4......Page 189 4 The Josefson–Nissenzweig Property for Cp-Spaces, Metrizable Quotients......Page 191 References......Page 194 1 Introduction......Page 196 1.1 (n+1)-Tensor Norms......Page 197 1.2 n-Linear Operator Ideals......Page 201 1.3 Some Preliminary Results......Page 203 2 αCr-Integral Operators......Page 206 2.1 Ultrapowers of Spaces ellp[ellq]......Page 209 2.2 Building the Measure Spaces......Page 212 2.3 Completing the Operators of the Global Diagram......Page 222 References......Page 228 1 Introduction......Page 230 2 Some Characterizations......Page 232 3 The Property SLD in Some Classes of Compacta K......Page 235 References......Page 244 1 Introduction......Page 246 2 The Functions fn and gn......Page 249 3 The Fixed Points of fn and the Sets Rζn(z)......Page 258 4 The Fixed Point Theory and the Maximum Density Interval for ζn(z)......Page 264 5 Numerical Experiences......Page 267 References......Page 270 1 Notation and Terminology......Page 272 2 Lindelöf Spaces......Page 273 2.1 The Lindelöf Number......Page 275 3.1 Definition and First Properties......Page 277 3.2 Generalizing Lindelöf Σ-Spaces......Page 278 3.3 Lindelöf Σ-Spaces in Cp-Theory......Page 279 4 Characterizing When νX Is a Lindelöf Σ-Space......Page 285 References......Page 287 1 Preliminaries......Page 289 1.2 Tensor Products and Tensor Norms......Page 291 1.3 Ultraproducts......Page 293 1.5 The mathcalLp-Spaces of Lindenstrauss and Pelczyǹski......Page 294 2 The Class of mathcalLλ-Spaces......Page 295 3 DPR-Local Unconditional Structure: The Class of the Quasi-mathcalLλ-Spaces......Page 296 4 (GL)-Local Unconditional Structure: The Class of mathcalLλ,g-Spaces......Page 299 References......Page 301 This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel López-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas.-- Provided by publisher This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel Lâopez-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel LÃ3pez-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas