Vector Measures, Integration and Related Topics (Operator Theory: Advances and Applications, 201)

Title page
Copyright  Page
Table of Contents
Preface
List of Talks
On Mean Ergodic Operators
	1. Introduction
	2. Preliminary results
	3. Mean ergodic results
	References
Fourier Series in Banach spaces and
Maximal Regularity
	0. Introduction
	1. Vector-valued Fourier series and operator-valued
Fourier multipliers
	2. The Marcinkiewicz multiplier theorem in the general case
	3. The periodic non-homogeneous problems
	4. Maximal regularity
	5. The non-autonomous equations
	References
Spectral Measures on Compacts of
Characters of a Semigroup
	1. Introduction
	2. A Berg-Maserick type theorem
		2.1. Definitions and notations
		2.2. The Berg-Maserick type theorem
	3. An integral representation via spectral measures
	4. Examples of ∗-representations
	5. A construction of the spectral measure
	6. The Gelfand-Naimark theorem for abelian C∗-algebras
	References
On Vector Measures, Uniform Integrability
and Orlicz Spaces
	1. Introduction and preliminaries
	2. The results
	References
The Bohr Radius of a Banach Space
	1. Introduction and preliminaries
	References
Spaces of Operator-valued Functions Measurable with Respect to
the Strong Operator Topology
	1. Introduction
	2. Strong μ-normability of operator-valued functions
	3. Spaces of operator-valued functions
	References
Defining Limits by Means of Integrals
	1. Introduction
	2. Preliminaries
	3. I-convergence in Riesz spaces
	4. Applications
	References
A First Return Examination
of Vector-valued Integrals
	1. Introduction
	2. Preliminaries
	3. Bochner integrable functions
	4. Pettis integrable functions
	References
A Note on Bi-orthomorphisms
	1. Introduction
	2. Preliminaries
	3. Separately disjointness preserving operators
	References
Compactness of Multiplication Operators on Spaces of Integrable Functions
with Respect to a Vector Measure
	1. Introduction
	2. Compactness and weak compactness
	References
Some Applications of Nonabsolute Integrals in the Theory of Differential Inclusions in Banach Spaces
	1. Introduction
	2. Multivalued integrals
	3. Results
	References
Equations Involving the Mean of
Almost Periodic Measures
	1. Introduction
	2. Preliminaries
	4. Equations with almost periodic measures and functions
	References
How Summable are Rademacher Series?
	1. Introduction: a problem on vector measures
	2. The Rademacher system
	3. A problem on function spaces
	4. The Rademacher multiplicator space
		4.1. The space Λ(R,X)
		4.2. The symmetric kernel of Λ(R,X)
		4.3. When is Λ(R,X) rearrangement invariant?
		4.4. Head and tail behavior
	5. An open question
	References
Rearrangement Invariant Optimal Domain for Monotone Kernel Operators
	1. Introduction
	2. Preliminaries
	3. R.i. optimal domain for T
	References
The Fubini and Tonelli Theorems
for Product Local Systems
	1. Introduction
	2. Preliminaries
	3. A convergence theorem for the S1-integral on the real line
	4. Product local system
	5. S-integral for a product local system
	6. The Fubini Theorem for a product local system
	References
A Decomposition of Henstock-Kurzweil-Pettis
Integrable Multifunctions
	Introduction
	1. Notations and preliminaries
	2. A decomposition theorem for HKP-integrable multifunctions
	References
Non-commutative Yosida-Hewitt Theorems and Singular Functionals in
Symmetric Spaces of τ-measurable Operators
	1. Introduction and preliminaries
	2. Preliminaries and notation
	3. Normed spaces of τ -measurable operators
		3.1. Normed M-bimodules
		3.2. Symmetrically normed M-bimodules and their K¨othe duals
		3.3. Normal and singular functionals on a normed M-bimodule
	4. The Yosida-Hewitt decomposition in M-bimodules
	5. Elements of order-continuous norm and singular functionals
	6. A vector-valued Yosida-Hewitt theorem
	References
Ideals of Subseries Convergence
and Copies of c0 in Banach Spaces
	References
On Operator-valued Measurable Functions
	1. Introduction
	2. Measurable operator-valued functions
		2.1. Strongly p-integrable functions
		2.2. Classes of (operator-valued) integral multiplier functions
		2.3. (p, q)-integral functions
		2.4. A new class of operator-valued functions
	References
Logarithms of Invertible Isometries, Spectral Decompositions and Ergodic Multipliers
	1. Introduction
	2. Logarithms of measures and translations
	3. Logarithms of invertible isometries
	4. Trigonometrically well-bounded operators
	5. Trigonometrically well-bounded operators on super-reflexive
spaces and norm growth of iterates
	References
Norms Related to Binomial Series
	0. Introduction
	1. Generalities
	2. 2-norm
	3. 3-norm
	4. H as an operator
	5. Further ideal properties
	References
Vector-valued Extension of Linear Operators, 
and Tb Theorems
	1. Introduction
	2. Review of the proof of the Tb theorem
	3. Probabilistic approach to the paraproduct
	References
Some Recent Applications
of Bilinear Integration
	1. Introduction
	2. Bilinear integration in tensor products
	3. Random evolutions
	4. Scattering theory
	5. Bilinear integration with respect to white noise
	References
A Complete Classification of Short
Symmetric-antisymmetric Multiwavelets
	1. Introduction
	2. Multiwavelets
	3. Multiwavelets with three taps
	4. Multiwavelets with four taps
	References
On the Range of a Vector Measure
	1. Introduction
	2. Preliminaries
	3. Main results
	References
Measure and Integration: Characterization
of the New Maximal Contents and Measures
	1. The relevant properties of contents and measures
		1.1 Lemma.
		1.2 Remark.
		1.3 Proposition.
		1.4 Theorem.
		1.5 Example.
	2. The characterization theorems
		2.1 Inner Remark.
		2.2 Continuation.
		2.3 Outer Remark.
		2.4 Outer Characterization Theorem.
		2.5 Remark.
	3. Another inner characterization theorem
		3.1 Theorem.
		3.2 Theorem.
		3.3 Inner Characterization Theorem.
	4. Application to the inner measure constructions
		4.1 Example.
	References
Vector Measures of Bounded γ-variation
and Stochastic Integrals
	1. Introduction
	2. Vector measures of bounded γ-variation
	References
Does a Compact Operator Admit a Maximal
Domain for its Compact Linear Extension?
	1. Introduction
	2. Proof of Theorem 1.1
	3. Weakly compact linear extension
	References
A Note on R-boundedness in Bidual Spaces
	References
Salem Sets in the p-adics, the Fourier  Restriction Phenomenon and Optimal 
Extension of the Hausdorff-Young Inequality
	1. Introduction
	2. p-adic Salem sets and the L2-Fourier restriction phenomenon
	3. Optimal extension of the Hausdorff-Young inequality in Zp
	References
L-embedded Banach Spaces and
a Weak Version of Phillips Lemma
	References
When is the Space of Compact Range Measures
Complemented in the Space of All Vector-valued Measures?
	1. Introduction
		1.1. Complementability
		1.2. Notation
		1.3. Main result
	2. Proof of Theorem 1.1: the separable case
		2.1. Recalling why c0 is not complemented in l∞
		2.2. Identifying measures and operators
		2.3. Rademacher functions
		2.4. Walsh system
	3. Proof in the non separable case
	References
When is the Optimal Domain of a Positive 
Linear Operator a Weighted L1-space?
	1. Introduction
	2. The L0 case
	3. The Banach function space case
	4. Examples
	References
Liapounoff Convexity-type Theorems
	1. Introduction
	2. Definitions and notation
	3. Example
	4. Non-negative scalar measures
	5. Vector measures
	6. Liapounoff convexity-type theorems
	References
List of Participants