CONTEMPORARY MATHEMATICS

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1 CONTEMPORARY MATHEMATICS 328 Function Spaces Fourth Conference on Function Spaces May 14-19,2002 Southern Illinois University at Edwardsville Krzysztof Jarosz Editor

2 CoNTEMPORARY MATHEMATICS 328 Function Spaces Fourth Conference on Function Spaces May 14-19, 2002 Southern Illinois University at Edwardsville Krzysztof Jarosz Editor American Mathematical Society Providence, Rhode Island

3 Editorial Board Dennis DeTurck, managing editor Andreas Blass Andy R. Magid Michael Vogelius This volume contains the proceedings of the Fourth Conference on Function Spaces, held May 14~ 19, 2002, at Southern Illinois University at Edwardsville Mathematics Subject Classification. Primary 32H02, 46E25, 46H05, 46J10, 46J15, 46L07, 47 AlO, 47B38, 47L10, 54D05. Library of Congress Cataloging-in-Publication Data Conference on Function Space (4th : 2002 : Southern Illinois University at Edwardsville) Function spaces : Fourth Conference on Function Spaces, May 14-19, 2002, Southern Illinois University at Edwardsville / Krzysztof Jarosz, editor. p. em. -(Contemporary mathematics, ISSN ; 328) Includes bibliographical references. ISBN (softcover: alk. paper) 1. Function spaces-congresses. I. Jarosz, Krzysztof, 1953~ II. Title. III. Contemporary mathematics (American Mathematical Society) ; v. 328 QA323.C '.73-dc Copying and reprinting. Material in this book may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island , USA. Requests can also be made by to reprint-permissien@ams. erg. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) 2003 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http: I /www. ams. erg/

4 Contents Preface v Components of resolvent sets and local spectral theory PIETRO AlENA AND FERNANDO VILLAFANE 1 The Fejer-Riesz inequality and the index of the shift JOHN R. AKEROYD 15 A Cauchy-Green formula on the unit sphere in C 2 JOHN T. ANDERSON AND JOHN WERMER 21 On a-dual algebras HUGO ARIZMENDI, ANGEL CARRILLO, AND LOURDES PALACIOS 31 A connected metric space that is not separably connected RICHARD M. ARON AND MANUEL MAESTRE 39 Weighted Chebyshev centres and intersection properties of balls in Banach spaces PRADIPTA BANDYOPADHYAY AND S. DUTTA 43 The boundary of the unit ball in H 1 -type spaces PAUL BENEKER AND JAN WIEGERINCK 59 Complete isometries - an illustration of noncommutative functional analysis DAVID P. BLECHER AND DAMON M. HAY 85 Some recent trends and advances in certain lattice ordered algebras KARIM BOULABIAR, GERARD BUSKES, AND ABDELMAJID TRIKI 99 An extension of a theorem of Wermer, Bernard, Sidney and Hatori to algebras of functions on locally compact spaces EGGERT BRIEM 135 Some mapping properties of p-summing operators with Hilbertian domain QrNGYING Bu 145 The unique decomposition property and the Banach-Stone theorem AUDREY CURNOCK, JOHN HOWROYD, AND NGAI-CHING WONG 151 A survey of algebraic extensions of commutative, unital normed algebras THOMAS DAWSON 157 iii

5 iv CONTENTS Some more examples of subsets of c 0 and 1 [0, 1] failing the fixed point property P. N. DOWLING, C. J. LENNARD, AND B. TURETT 171 Homotopic composition operators on H 00 ( Bn) PAMELA GORKIN, RAYMOND MORTINI, AND DANIEL SUAREZ 177 Characterization of conditional expectation in terms of positive projections J. J. GROBLER AND M. DE KocK 189 The Krull nature of locally C* -algebras MARINA HARALAMPIDOU 195 Characterizations and automatic linearity for ring homomorphisms on algebras of functions 0SAMU HATORI, TAKASHI ISHII, TAKESHI MIURA, AND SIN-EI TAKAHASI 201 Carleson embeddings for weighted Bergman spaces HANS JARCHOW AND URS KOLLBRUNNER 217 Weak* -extreme points of injective tensor product spaces KRZYSZTOF JAROSZ AND T. S. S. R. K. RAO 231 Determining sets and fixed points for holomorphic endomorphisms KANG-TAE KIM AND STEVEN G. KRANTZ 239 Localization in the spectral theory of operators on Banach spaces T. L. MILLER, v. G. MILLER, AND M. M. NEUMANN 247 Abstract harmonic analysis, homological algebra, and operator spaces VOLKER RUNDE 263 Relative tensor products for modules over von Neumann algebras DAVID SHERMAN 275 Uniform algebras generated by unimodular functions STUART J. SIDNEY 293 Analytic functions on compact groups and their applications to almost periodic functions THOMAS TONEY AND S. A. GRIGORYAN 299

6 Preface The Fourth Conference on Function Spaces was held at Southern Illinois University at Edwardsville from May 14 to May 19, It was attended by over 100 participants from 25 countries. The lectures covered a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), P-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The main purpose of the conference was to bring together mathematicians interested in various problems within the general area of function spaces and to allow a free discussion and exchange of ideas with people working on exactly the same problems as well as with people working on related questions. Hence, most of the lectures, and therefore the papers in this volume, have been directed to non-experts. A number of articles contain an exposition of known results (known to experts) and open problems; other articles contain new discoveries that are presented in a way that should be accessible also to mathematicians working in different areas of function spaces. The conference was the fourth in a sequence of conferences on function spaces at SlUE, with the first held in the spring of 1990, the second in the spring of 1994, and the third one in the spring of The proceedings of the first two conferences were published with Marcel Dekker in the Lecture Notes in Pure and Applied Mathematics series ( #136 and #172); the proceedings of the third conference were published by the AMS in the Contemporary Mathematics series (#232). The abstracts, the schedule of the talks, and other information, as well as the pictures of the participants, are available on the conference Web page at The conference was sponsored by grants from Southern Illinois University and from the National Science Foundation. The editor would like to thank everyone who contributed to the proceedings: the authors, the referees, the sponsoring institutions, and the American Mathematical Society. The editor would also like to express very special thanks to his wife, Dorota, for her active professional help during all of the stages of the organization - without her help the conference and the proceedings would not have been possible. Krzysztof Jarosz v

7 This volume presents papers from the Fourth Conference on Function Spaces. The lectures covered a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), LP-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and related subjects. Included are 26 articles written by leading experts. Known results, open problems, and new discoveries are featured. Most papers are written for nonexperts, so the book can serve as a good introduction to the material presented. ISBN CONM/328