**Contemporary Mathematics**

Volume: 85;
1989;
521 pp;
Softcover

MSC: Primary 46;

**Print ISBN: 978-0-8218-5092-3
Product Code: CONM/85**

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

**Electronic ISBN: 978-0-8218-7673-2
Product Code: CONM/85.E**

List Price: $75.00

AMS Member Price: $60.00

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# Banach Space Theory

Share this page *Edited by *
*Bor-Luh Lin*

This volume contains the proceedings from a Research Workshop on Banach Space Theory held at the University of Iowa in Iowa City in July 1987. The workshop provided participants with a collaborative working atmosphere in which ideas could be exchanged informally. Several papers were initiated during the workshop and are presented here in their final form. Also included are contributions from several experts who were unable to attend the workshop. None of the papers will be published elsewhere. During the workshop, two hours each day were devoted to seminars on current problems in such areas as weak Hilbert spaces, zonoids, analytic martingales, and operator theory, and these topics are reflected in some of the papers in the collection.

# Table of Contents

## Banach Space Theory

- Contents vii8 free
- Preface ix10 free
- Workshop Participants xi12 free
- Titles of seminars given during the Workshop xiii14 free
- Isometries of James space 116 free
- Quasi-reflexive and tree spaces constructed in the spirit of R. C. James 1934
- Projections onto block bases 4560
- The Schroeder–Bernstein property for Banach spaces 6176
- Rotund reflexive Orlicz spaces are fully convex 7994
- Biorthogonal systems and big quotient spaces 87102
- Analytic martingales and plurisubharmonic barriers in complex Banach spaces 111126
- Existence and uniqueness of isometric preduals: A survey 131146
- 0. Introduction – Notation. 132147
- I. Applications of the Hahn–Banach theorem: some basic lemmas. 134149
- II. Existence and uniqueness of preduals for a first family of "smooth" spaces. 140155
- Ill. An alternative approach: the ball topology. 149164
- IV. A critical example: the space L1. 153168
- V. Uniqueness of preduals for a second family of spaces. 155170
- VI. Stability properties of the class of unique preduals. 163178
- VII. Automatic ω* –continuity – Applications. 166181
- VIII. More non–trivial conditions for the existence or the characterization of the predual. 175190
- IX. Spaces which are not unique preduals and other counterexamples. 183198
- X. Open problems. 185200

- The ball topology and its applications 195210
- On the closedness of the sum of closed operators on a UMD space 239254
- Ultrapowers of rearrangement-invariant function spaces I 253268
- KMP, RNP, and PCP for Banach spaces 281296
- Independence in separable Banach spaces 319334
- On the weak* -fixed point property 325340
- Some geometrical and topological properties of the unit sphere in a normed linear space 339354
- The λ-function in Banach spaces 345360
- Smooth functions in Orlicz spaces 355370
- Fefferman spaces and C* -algebras 371386
- J H* has the PCP 387402
- An analogue of the F. and M. Riesz theorem for spaces of differential functions 405420
- Almost isometric methods in some isomorphic embedding problems 427442
- Sub-simplexes of convex sets and some characterizations of simplexes with the RNP 447462
- Some more remarkable properties of the James-tree space 465480
- A note on the Lavrientiev index for the quasi-reflexive Banach spaces 497512
- ω-independence in non separable Banach spaces 509524
- The canonical injection for C([0, 1]) into L2,1 is not of cotype 2 513528