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Vector Measures, Integration and Related Topics

:	Werner J. Ricker, Gerd Mockenhaupt, Guillermo P. Curbera
:	Guillermo Curbera, Gerd Mockenhaupt, Werner J. Ricker
:	Vector Measures, Integration and Related Topics
:	Birkhäuser Basel
:	9783034602112
:	1
:	CHF 132.90
:

:	Analysis
:	English

:	382
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This volume contains a selection of articles on the theme"vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in the area and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, and functional analysis. The material is of interest to experts, young researchers and postgraduate students.

	Table of Contents	6
	Preface	9
	List of Talks	11
	On Mean Ergodic Operators	15
	1. Introduction	15
	2. Preliminary results	17
	3. Mean ergodic results	21
	References	33
	Fourier Series in Banach spaces andMaximal Regularity	35
	0. Introduction	35
	1. Vector-valued Fourier series and operator-valuedFourier multipliers	36
	2. The Marcinkiewicz multiplier theorem in the general case	44
	3. The periodic non-homogeneous problems	45
	4. Maximal regularity	46
	5. The non-autonomous equations	50
	References	52
	Spectral Measures on Compacts ofCharacters of a Semigroup	54
	1. Introduction	54
	2. A Berg-Maserick type theorem	55
	2.1. Definitions and notations	55
	2.2. The Berg-Maserick type theorem	56
	3. An integral representation via spectral measures	57
	4. Examples of *-representations	58
	5. A construction of the spectral measure	60
	6. The Gelfand-Naimark theorem for abelian C*-algebras	61
	References	62
	On Vector Measures, Uniform Integrabilityand Orlicz Spaces	63
	1. Introduction and preliminaries	63
	2. The results	65
	References	69
	The Bohr Radius of a Banach Space	70
	1. Introduction and preliminaries	70
	References	75
	Spaces of Operator-valued Functions Measurable with Respect tothe Strong Operator Topology	76
	1. Introduction	76
	2. Strong µ-normability of operator-valued functions	78
	3. Spaces of operator-valued functions	83
	References	89
	Defining Limits by Means of Integrals	90
	1. Introduction	90
	2. Preliminaries	90
	3. I-convergence in Riesz spaces	92
	4. Applications	95
	References	97
	A First Return Examinationof Vector-valued Integrals	99
	1. Introduction	99
	2. Preliminaries	100
	3. Bochner integrable functions	101
	4. Pettis integrable functions	104
	References	107
	A Note on Bi-orthomorphisms	108
	1. Introduction	108
	2. Preliminaries	109
	3. Separately disjointness preserving operators	111
	References	116
	Compactness of Multiplication Operators on Spaces of Integrable Functionswith Respect to a Vector Measure	117
	1. Introduction	117
	2. Compactness and weak compactness	118
	References	121
	Some Applications of Nonabsolute Integrals in the Theory of Differential Inclusions in Banach Spaces	122
	1. Introduction	122
	2. Multivalued integrals	123
	3. Results	125
	References	130
	Equations Involving the Mean ofAlmost Periodic Measures	132
	1. Introduction	132
	2. Preliminaries	133
	3. Properties of the almost periodic functions	135
	4. Equations with almost periodic measures and functions	137
	References	140
	How Summable are Rademacher Series?	141
	1. Introduction: a problem on vector measures	141
	2. The Rademacher system	142
	3. A problem on function spaces	144
	4. The Rademacher multiplicator space	145
	4.1. The space .(R,X)	145
	4.2. The symmetric kernel of .(R,X)	147
	4.3. When is .(R,X) rearrangement invariant?	149
	4.4. Head and tail behavior	152
	5. An open question	153
	References	153
	Rearrangement Invariant Optimal Domain for Monotone Kernel Operators	155
	1. Introduction	155
	2. Preliminaries	156
	3. R.i. optimal domain for T	157
	References	163
	The Fubini and Tonelli Theoremsfor Product Local Systems	165
	1. Introduction	165
	2. Preliminaries	166
	3. A convergence theorem for the S1-integral on the real line	167
	4. Product local system	169
	5. S-integral for a product local system	170
	6. The Fubini Theorem for a product local system	172
	References	176
	A Decomposition of Henstock-Kurzweil-PettisIntegrable Multifunctions	177
	Introduction	177
	1. Notations and preliminaries	178
	2. A decomposition theorem for HKP-integrable multifunctions	181
	References	187
	Non-commutative Yosida-Hewitt Theorems and Singular Functionals inSymmetric Spaces of t-measurable Operators	189
	1. Introduction and preliminaries	189
	2. Preliminaries and notation	190
	3. Normed spaces of t -measurable operators	193
	3.1. Normed M-bimodules	193
	3.2. Symmetrically normed M-bimodules and their K¨othe duals	193
	3.3. Normal and singular functionals on a normed M-bimodule	195
	4. The Yosida-Hewitt decomposition in M-bimodules	196
	5. Elements of order-continuous norm and singular functionals	198
	6. A vector-valued Yosida-Hewitt theorem	199
	References	203
	Ideals of Subseries Convergenceand Copies of c0 in Banach Spaces	205
	References	209
	On Operator-valued Measurable Functions	211
	1. Introduction	211
	2. Measurable operator-valued functions	212
	2.1. Strongly p-integrable functions	213
	2.2. Classes of (operator-valued) integral multiplier functions	215
	2.3. (p, q)-integral functions	216
	2.4. A new class of operator-valued functions	217
	Refe