Joram Lindenstrauss
Encyclopedia
Joram Lindenstrauss (born October 28, 1936) is an Israel
i mathematician
working in functional analysis
. He is professor emeritus of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem
, Israel
.
from the Hebrew University (dissertation: Extension of Compact Operators
, advisors: Aryeh Dvoretzky
, Branko Grünbaum
). He joined the faculty of the university in 1965 and worked in various areas of functional analysis
and geometry
. His son Elon Lindenstrauss
is also a mathematician.
and many theorems of Lindenstrauss: For example, in a Banach space
with the Radon–Nikodym property, a closed
and bounded set
has an extreme point
; compactness
is not needed.
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
i mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
. He is professor emeritus of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
, Israel
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
.
Biography
In 1962, Lindenstrauss earned his Ph.D.Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from the Hebrew University (dissertation: Extension of Compact Operators
Compact operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y...
, advisors: Aryeh Dvoretzky
Aryeh Dvoretzky
Aryeh Dvoretzky was a Russian-born Israeli mathematician, the winner of the 1973 Israel Prize in Mathematics. He is best known for his work in functional analysis, statistics and probability.-Biography:...
, Branko Grünbaum
Branko Grünbaum
Branko Grünbaum is a Croatian-born mathematician and a professor emeritus at the University of Washington in Seattle. He received his Ph.D. in 1957 from Hebrew University of Jerusalem in Israel....
). He joined the faculty of the university in 1965 and worked in various areas of functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
and geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. His son Elon Lindenstrauss
Elon Lindenstrauss
Elon Lindenstrauss is an Israeli mathematician, and a winner of the 2010 Fields Medal.Since 2004, he has been a professor at Princeton University...
is also a mathematician.
Research
He is a namesake of the Johnson–Lindenstrauss lemmaJohnson–Lindenstrauss lemma
In mathematics, the Johnson–Lindenstrauss lemma is a result concerning low-distortion embeddings of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a small set of points in a high-dimensional space can be embedded into a space of much lower dimension in such...
and many theorems of Lindenstrauss: For example, in a Banach space
Banach space
In mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...
with the Radon–Nikodym property, a closed
Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points...
and bounded set
Bounded set
In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called unbounded...
has an extreme point
Extreme point
In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S...
; compactness
Compact space
In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...
is not needed.
Published works
- Classical Banach spaces (with Lior Tzafriri). Hebrew University of Jerusalem, 1973
- Classical Banach spaces II (with Lior Tzafriri). University of CopenhagenUniversity of CopenhagenThe University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
, Institute of Mathematics,1978 - Banach spaces with a unique unconditional basis, up to permutation (with Jean BourgainJean BourgainJean Bourgain is a Belgian mathematician. He has been a faculty member at the University of Illinois, Urbana-Champaign and, from 1985 until 1995, professor at Institut des Hautes Études Scientifiques at Bures-sur-Yvette in France, and since 1994 at the Institute for Advanced Study in Princeton,...
, Peter George Casazza, and Lior Tzafriri). Memoirs of the American Mathematical Society, vol 322. American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
, 1985 - Geometric nonlinear functional analysis (with Yoav Benyamini). Colloquium publications, 48. American Mathematical Society