Topics in Banach Space Theory

Fernando Albiac · Nigel J. Kalton

2006-ж. май · Graduate Texts in Mathematics 233-китеп · Springer Science & Business Media

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This book grew out of a one-semester course given by the second author in 2001 and a subsequent two-semester course in 2004-2005, both at the Univ- sity of Missouri-Columbia. The text is intended for a graduate student who has already had a basic introduction to functional analysis; the aim is to give a reasonably brief and self-contained introduction to classical Banach space theory. Banach space theory has advanced dramatically in the last 50 years and webelievethatthetechniquesthathavebeendevelopedareverypowerfuland should be widely disseminated amongst analysts in general and not restricted to a small group of specialists. Therefore we hope that this book will also prove of interest to an audience who may not wish to pursue research in this area but still would like to understand what is known about the structure of the classical spaces. Classical Banach space theory developed as an attempt to answer very natural questions on the structure of Banach spaces; many of these questions date back to the work of Banach and his school in Lvov. It enjoyed, perhaps, its golden period between 1950 and 1980, culminating in the de?nitive books by Lindenstrauss and Tzafriri [138] and [139], in 1977 and 1979 respectively. The subject is still very much alive but the reader will see that much of the basic groundwork was done in this period.