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The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it es...
This is a new release of the original 1924 edition.
Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional ...
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Czasy i przyja nie" to zbior barwnych opowie ci, w ktorych autor opisuje sp dzone na Lubelszczy nie dzieci stwo, pierwsze kroki stawiane w zawodzie pilota, burzliwe wydarzenia wojenne oraz lata sp dzone na emigracji. Nie jest to jednak wy cznie ksi ka wspomnieniowa, bowiem na przyk adzie biografii jednego cz owieka mowi ona o zawik anych i dramatycznych kartach najnowszej historii Polski i wiata. Czytelnik znajdzie w niej rownie portrety ludzi, ktorzy przeszli do dziejow polskiego lotnictwa, pisarzy, aktorow i intelektualistow, jakimi szczyci a si nasza emigracja. ***** "Times and Friendships," is a collection of colourful accounts, describing a childhood spent in the Lublin district, Poland, the author's first steps as a professional pilot, the upheavals of war and the years spent in exile. One man's biography becomes a journey through the intricate and dramatic pathways of the recent history of Poland and the world, with portraits of Polish aviators, writers, actors and intellectuals.
Argues that many episodes of transformational crisis have been misdiagnosed as mental illness, and explains how to use such a crisis for spiritual development.
Papers presented at the International Conference on History of Mathematical Sciences, held at New Delhi during 20-23 December 2001.
This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's [Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's [T-Jl] where operator ideals and distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's [Pie].
An introduction to Jewish beliefs and practices, demonstrating that Judaism is a living religion which retains the vitality found in the Biblical corpus, but which has gone on to develop institutions, modes of behaviour and ideas which constitute the singularity of Jewish expression.