**Joram Lindenstrauss**was the son of Bruno Lindenstrauss and Ilse Stammreich. Bruno Lindenstrauss (1908-1968), born in Berlin on 25 January 1908, was a lawyer and his wife Ilse Stammreich (1903-2000), born in Berlin on 19 August 1903, was also a lawyer. When the Nazis came to power in Germany in 1933 with their extreme anti-Semitic policies, the Jewish couple Bruno and Ilse Lindenstrauss emigrated to Palestine. We note that Ilse Lindenstrauss wrote

*On women's law in Israel*, which was published in Tel-Aviv by the Women's International Zionist Organisation, Instruction and Information Centre in 1949. Joram was their only son, attending school in Tel Aviv.

Lindenstrauss began his studies in mathematics at the Hebrew University of Jerusalem in 1954. At this stage he was only a part-time student for he was also undertaking his compulsory military service. After spending two years with only part-time study, in 1956, with his military service completed, he became a full-time student. He received his Master's degree from the Hebrew University of Jerusalem in 1959 and continued to study there for his Ph.D. advised by Aryeh Dvoretzky and Branko Grünbaum. His first publication, which appeared in the Bulletin of the Research Council of Israel Section F, was *On some subspaces of* *l*^{1} *and* *c*_{0}. This was published in 1961 while he was still working on his thesis.

He submitted his thesis *Extension of Compact Operators* to the Hebrew University of Jerusalem and was awarded his Ph.D. in 1962. The main results of his thesis appeared in a number of places. He announced the results in Technical Note No. 22 (Jerusalem, 1961) and in a modified form in his note *On the Extension Property for Compact Operators* (1962) in the *Bulletin* of the American Mathematical Society. In this note he acknowledged that:-

He also writes:-The research reported in this note has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command U.S. Air Force through its European Office.

Proofs of the results stated in the paper appear in his thesis and also inThis note is based on a part of a Ph.D. thesis which was written under the supervision of Professor A Dvoretzky and Dr B Grünbaum. I wish to express my warm thanks to both for their valuable help and kind encouragement.

*The*

*Extension of Compact Operators*I, II, III

*, Technical Notes Nos.*28, 31, 32 (Jerusalem, 1962).

While studying at the Hebrew University of Jerusalem, Lindenstrauss met Naomi Zelinger; they married and had four children Ayelet, Elon (born 1970), Kinneret (born 1972), and Gallia. Ayelet Lindenstrauss Larsen and Elon Lindenstrauss both became mathematicians, Ayelet is Professor of Mathematics at Indiana University, Bloomington, while Elon achieved the highest mathematical award when he was awarded the Fields Medal in 2010. Kinneret Lindenstrauss Keren is a biophysicist, at Technion winning the Krill prize for Scientific Research from the Wolf Foundation in 2010, while Gallia is a researcher at the Institute for National Security Studies at Tel Aviv University.

After the award of his Ph.D. Lindenstrauss spent three years in the United States, first at Yale University and later at the University of Washington in Seattle, working there between 1962 and 1965. He entered the United States on 26 August 1962 with his wife, having flown on a Pan Am flight from London. His daughter Ayelet writes [4]:-

During his time in the United States wrote many papers.The boy who grew up in Israel and left it for the first time after completing his PhD never ceased to marvel at being a member of the international fellowship of mathematics.

*Some results on the extension of operators*appeared in 1963, and in it he notes that it is closely related to work in his thesis. He thanks Shizuo Kakutani, who was on the faculty of Yale:-

Lindenstrauss also thanks Shizuo Kakutani for "valuable discussions" concerning... for many valuable discussions concerning the subject of this note.

*On a problem of Nachbin concerning extension of operators*, also published in 1963. His paper

*On operators which attain their norm*(1963) was written after "valuable discussions" with Robert Ralph Phelps (1926-2013) who had been appointed to the University of Washington in 1962. Lindenstrauss published two further papers in 1963 and seven in 1964, one of which was

*On nonlinear projections in Banach spaces*(1964) [6]:-

His 2-page paperIn this work he proved theorems that exhibit remarkable, and arguably unexpected, rigidity phenomena for Banach spaces when they are deformed by uniformly continuous(or Lipschitz)mappings.

*A short proof of Liapounoff's convexity theorem*(1966) has led to this beautiful proof becoming standard in functional analysis texts as well as becoming important for further developments of the topic. We note that by 1966, Lindenstrauss had published around 30 papers, a truly remarkable achievement for someone 30 years of age.

Lindenstrauss left the United States and, back in Israel in 1965, he became a senior lecturer at the Hebrew University and worked at the Einstein Institute of Mathematics. Yoav Benyamini writes [4]:-

Lindenstrauss was promoted to associate professor in 1967 and to full professor in 1969. He was named Leon H and Ada G Miller Memorial Professor of Mathematics in 1985.In1965Joram Lindenstrauss joined the Hebrew University as a new faculty, and I was a third-year undergraduate student sitting in his Banach Spaces course. This first encounter set the course of my life. The Banach space group in Jerusalem began with Dvoretzky, who was joined by his former student Grünbaum and their students. A phase transition occurred with the arrival of Joram, who joined Dvoretzky in the supervision of the doctoral theses of Lazar and Zippin, and Joram's influence dominated their work. ... I started to work with him on a master's thesis in1966. Joram gave excellent basic and advanced courses, and within a few years the list of his students grew very fast ... Joram's supervision style was very "open." We did not have orderly weekly meetings, and he never gave me a problem for the thesis. The exposure to the different directions and problems came through his comments and criticism in the seminar and other discussions. This is also how I learned how to judge what is "important," "interesting," what is worthwhile to read, and what is publishable. His approach and views were so dominant that he was "heard" even when he was not present. Joram was very systematic and methodical. His answers to questions sounded like he had prepared a lecture on the subject. He did not like to discuss speculations: he would send me to write up my ideas and, of course, in most cases the speculation led nowhere. But when I did hand him something in writing, he was a wonderful reader. It would come back the next day with detailed feedback. He was also a wonderful writer, and his papers, books, and lecture notes(in Hebrew)are written in his typical systematic, clear, and concise style.

William B Johnson writes in [4]:-

Lindenstrauss published the lecture notesIn the1970s Joram's family spent several summers in Columbus(I was at Ohio State then), and my family spent one year in Jerusalem. In1981-82both families were in College Station, where Joram and I took our sabbaticals and Joram's wife, Naomi, worked on her PhD in computer science. Our wives became close friends and our children grew up together. Once when we went for Shabbat dinner at the Lindenstrauss home, Joram, with some help from Ayelet and Elon, built a Lego city in their living room. Our son was always happy to return to "Joram's toy store." Later I was a coach of a soccer team on which my son and Joram's daughter played, and I played basketball with Kinneret and some of her boy friends. Kinneret, now well known in the biophysics community, was the best player on the court and had a successful second career as a professional basketball player. Shabbat dinners at the Lindenstrauss home after our children were grown were particularly enjoyable when some of their children were present. It was great to get to know the adult Gallia, the youngest and most widely read of the Lindenstrauss clan(Google her to find out why), who was often present helping Naomi with the preparations.

*Classical Banach spaces*(1973) which he wrote jointly with Lior Tzafriri. The authors write in the Preface:-

Grahame Bennett writes in the review [1]:-The main purpose of these lecture notes is to give an outline of that part of Banach space theory which deals with properties of special and important classes of spaces. We have tried to present the main methods used in the theory, as well as the principal ideas involved in the proofs of the basic results. The lecture notes contain some well known and classical theorems but the main subject matter consists of recent results and research directions. Many open problems are mentioned throughout these notes.

The two authors expanded their lecture notes into two volumesBanach space theory has seen considerable change in recent years and these excellent lecture notes provide a highly readable and up-to-date survey of this area.

*Classical Banach spaces. I. Sequence spaces*(1977) and

*Classical Banach spaces. II. Function spaces*(1979). The authors write in the first of these volumes:-

The authors of [6] give the following overview of Lindenstrauss's achievements:-The purpose of this book is to present the main results and current research directions in the geometry of Banach spaces with an emphasis on the study of the structure of the classical Banach spaces, that isC(K)andL_{p}(μ)and related spaces. We do not attempt to write a comprehensive survey of Banach space theory, or even only of the theory of classical Banach spaces, since the amount of interesting results on the subject makes such a survey practically impossible. A part of the subject matter of this book appeared in outline in our lecture notes(1973). In contrast to those notes most of the results presented here are given with complete proofs. We therefore hope that it will be possible to use the present book as a textbook on Banach space theory and as a reference book for research workers in the area. It contains much material which was not discussed in the earlier version(1973), a large part of which is the result of very recent research work. An indication of the rapid recent progress in Banach space theory is the fact that most of the many problems stated in the earlier book have been solved by now.

Elon Lindenstrauss writes in [4] about his father:-A deep, original, clever and prolific mathematician, Joram Lindenstrauss ... was a pillar of modern functional analysis and an enormously influential champion of a tradition of excellence and uncompromising(at times, even harsh)pursuit of the highest possible quality of mathematical research. In addition to proving difficult theorems and solving longstanding open problems, Joram was a conceptual leader who was responsible for the formulation of foundational insights and major research directions that guided and shaped the intensive efforts of many researchers worldwide over several generations, and his legacy will undoubtedly continue to do so in the future.

David Preiss writes about interests of the Lindenstrauss family outside mathematics [4]:-My father was very honest, had high standards both for himself and for others, and always said exactly what he thought, regardless of whether what he thought was pleasant or unpleasant to hear. From the time I was a graduate student to the last talks of mine which he attended when I was already a well-established researcher, I was always especially nervous and tried to be very well prepared when giving a talk when he was in the audience, as I was sure I would be told afterwards exactly what he thought of the talk.

Gideon Schectman writes about Lindenstrauss's influence on him [4]:-I recall a number of non-mathematical events, such as playing basketball on a team opposing him(he was very good), going to concerts, his daughter Gallia's pictures of Jerusalem, walks in Jerusalem, exhibitions, and of course his welcoming family and the huge amount of help we were given by his wife, Naomi.

Lindenstrauss retired in 2005, having had poor health for some time, and after several years of deteriorating health he died in April 2012.What really set him apart from the point of view of his influence on me were the standards he set and lived by. He had very high standards as to what constitutes good mathematics and for scientific and personal integrity. These were also very easy to absorb from him: he always said what was on his mind whether asked for it or not.

Lindenstrauss received many honours for his outstanding mathematical contributions. He gave an invited lecture at the International Congress of Mathematicians in Nice in September 1970. He won the Israel Prize in Mathematics in 1981 and was elected as a member of the Israel Academy of Sciences in 1986. In 1997 he was the first non-Polish mathematician to receive the Banach Medal from the Polish Academy of Sciences. In 2000 he was elected to the Austrian Academy of Sciences and in 2001 he received an honorary doctorate from Kent State University in Ohio.

**Article by:** *J J O'Connor* and *E F Robertson*