Vector Measures, Integration and Related Topics

Slowly, but surely, it is becoming a tradition that biannual international conf- enceson"VectorMeasuresandIntegration"aretakingplace.The?rstmeetingwas held in Valencia (Spain) in 2004 with the respectable total of 35 participants and the second meeting in Sevilla (Spain) in 2006with 50 participants.It became clear at the latter meeting that there was already a broader interest level in the area generally(asitshouldbe).Relatedareasfromoperatortheory,functionalanalysis, Banach (and Fr' echet) spaces and lattices, non-commutative integration, function theory, classical and harmonic analysis, mathematical physics, and applied ma- ematics havetraditionallyused methods and techniquesfrom vector measuresand integration theory and, simultaneously, have themselves provided new problems, directions and impetus for the theory of vector measures and integration. So, for the third meeting, held in Eichst. att (Germany) in September 2008, a natural and deliberate step was taken to put a larger emphasis on applications andconnectionswith other areasofmathematics.Accordingly,the conferencetitle was modi?ed to "Vector Measures, Integration and Applications", which is also re?ected in the title of this volume. Correspondingly, the attendance grew to 84 participants, which illustrates that the area is really thriving. Most importantly, there was also a healthy mixture of "oldies" and younger researchers in att- dance, coming from 21 countries. In addition, there was a pleasant and interesting combination of abstract theory, concrete applications and open problems. Needless to say, the fourth meeting is already ?xed; it will take place in late 2010 in Murcia (Spain). Thisvolumeconsistsofaselectionofrefereedpapersbasedontalkspresented at the conference. The included papers represent rather well most of the topics covered in the conference.

Table of Contents:
On Mean Ergodic Operators.- Fourier Series in Banach spaces and Maximal Regularity.- Spectral Measures on Compacts of Characters of a Semigroup.- On Vector Measures, Uniform Integrability and Orlicz Spaces.- The Bohr Radius of a Banach Space.- Spaces of Operator-valued Functions Measurable with Respect to the Strong Operator Topology.- Defining Limits by Means of Integrals.- A First Return Examination of Vector-valued Integrals.- A Note on Bi-orthomorphisms.- Compactness of Multiplication Operators on Spaces of Integrable Functions with Respect to a Vector Measure.- Some Applications of Nonabsolute Integrals in the Theory of Differential Inclusions in Banach Spaces.- Equations Involving the Mean of Almost Periodic Measures.- How Summable are Rademacher Series?.- Rearrangement Invariant Optimal Domain for Monotone Kernel Operators.- The Fubini and Tonelli Theorems for Product Local Systems.- A Decomposition of Henstock-Kurzweil-Pettis Integrable Multifunctions.- Non-commutative Yosida-Hewitt Theorems and Singular Functionals in Symmetric Spaces of ?-measurable Operators.- Ideals of Subseries Convergence and Copies of c 0 in Banach Spaces.- On Operator-valued Measurable Functions.- Logarithms of Invertible Isometries, Spectral Decompositions and Ergodic Multipliers.- Norms Related to Binomial Series.- Vector-valued Extension of Linear Operators, and Tb Theorems.- Some Recent Applications of Bilinear Integration.- A Complete Classification of Short Symmetric-antisymmetric Multiwavelets.- On the Range of a Vector Measure.- Measure and Integration: Characterization of the New Maximal Contents and Measures.- Vector Measures of Bounded ?-variation and Stochastic Integrals.- Does a compact operator admit a maximal domain for its compact linear extension?.- A Note onR-boundedness in Bidual Spaces.- Salem Sets in the p-adics, the Fourier Restriction Phenomenon and Optimal Extension of the Hausdorff-Young Inequality.- L-embedded Banach Spaces and a Weak Version of Phillips Lemma.- When is the Space of Compact Range Measures Complemented in the Space of All Vector-valued Measures?.- When is the Optimal Domain of a Positive Linear Operator a Weighted L 1-space?.- Liapounoff Convexity-type Theorems.