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Methods in the Theory of Hereditarily Indecomposable Banach Spaces
A general method producing Hereditarily Indecomposable (H I) Banach spaces is provided. We apply this method to construct a nonseparable H I Banach space $Y$. This space is the dual, as well as the second dual, of a separable H I Banach space.
Atomic Boolean Subspace Lattices and Applications to the Theory of Bases
Those families of (closed) subspaces of a (real or complex) Banach space that arise as the set of atoms of an atomic Boolean algebra subspace lattice, abbreviated ABSL, are characterized. This characterization is used to obtain new examples of ABSL's including some with one-dimensional atoms. ABSL's with one-dimensional atoms arise precisely from strong [italic capital]M-bases. The strong rank one density problem for ABSL's is discussed and some affirmative results are presented. Several new areas of investigation in the theory of ABSL's are uncovered.
Introduction to Banach Spaces: Analysis and Probability
This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.
Handbook of Set-Theoretic Topology
This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.
Smooth Analysis in Banach Spaces
This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.
Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Mathematical Reviews
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