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A Course in Commutative Banach Algebras
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A Course in Commutative Banach Algebras

Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis.
 
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Tags: Banach, spaces, continuous, functions, compact
Optimization on Metric and Normed Spaces
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Optimization on Metric and Normed SpacesOptimization on Metric and Normed Spaces

The monograph is devoted to the study of optimization problems on complete metric spaces and Banach spaces.
 
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Tags: spaces, Banach, Optimization, Normed, Spaces, Optimization, spaces, Metric
Problems in Operator Theory (Graduate Studies in Mathematics)
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Problems in Operator Theory (Graduate Studies in Mathematics)Problems in Operator Theory (Graduate Studies in Mathematics)

This is one of the few books available in the literature that contains problems devoted entirely to the theory of operators on Banach spaces and Banach lattices. The book contains complete solutions to the more than 600 exercises in the companion volume, An Invitation to Operator Theory, Volume 50 in the AMS series Graduate Studies in Mathematics, also by Abramovich and Aliprantis.
 
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Tags: Studies, Banach, Theory, Operator, Mathematics, Graduate
Integral Representation Theory: Applications to Convexity, Banach Spaces and Potential Theory
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Integral Representation Theory: Applications to Convexity, Banach Spaces and Potential TheoryIntegral Representation Theory: Applications to Convexity, Banach Spaces and Potential TheoryThis monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet´s theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book

 
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Tags: theory, spaces, Banach, Theory, fairly, Integral, Potential
Stopping Time Techniques for Analysts and Probabilists
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Stopping Time Techniques for Analysts and ProbabilistsStopping Time Techniques for Analysts and Probabilists

This book considers convergence of adapted sequences of real and Banach space-valued integrable functions, emphasizing the use of stopping time techniques. Not only are highly specialized results given, but also elementary applications of these results. The book starts by discussing the convergence theory of martingales and sub-( or super-) martingales with values in a Banach space with or without the Radon-Nikodym property.
 
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Tags: martingales, results, space, Banach, convergence, Banach, martingales, Stopping