Robert Schatten (January 28, 1911 – August 26, 1977) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. Robert Schatten was born to a Jewish family in

Lviv Lviv ( or ; ; ; see #Names and symbols, below for other names) is the largest city in western Ukraine, as well as the List of cities in Ukraine, fifth-largest city in Ukraine, with a population of It serves as the administrative centre of ...

. His intellectual origins were at

Lwów School of Mathematics The Lwów school of mathematics () was a group of Polish mathematicians who worked in the interwar period in Lwów, Poland (since 1945 Lviv, Ukraine). The mathematicians often met at the famous Scottish Café to discuss mathematical problems, ...

, particularly well known for fundamental contributions to

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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

. His entire family was murdered during

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

, he himself emigrated to the

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

. In 1933 he got '' magister'' degree at Jan Kazimierz University of Lwów, and in 1939 he got master's degree at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

. Supervised by

Francis Joseph Murray Francis Joseph Murray (February 3, 1911 – March 15, 1996) was a mathematician, known for his foundational work (with John von Neumann) on functional analysis, and what subsequently became known as von Neumann algebras. He received his BA from C ...

, he got doctorate degree in 1942 for the thesis "''On the Direct Product of Banach Spaces''". Shortly after being appointed to a junior

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

ship, he joined the

United States army The United States Army (USA) is the primary Land warfare, land service branch of the United States Department of Defense. It is designated as the Army of the United States in the United States Constitution.Article II, section 2, clause 1 of th ...

where during training he suffered a back injury which affected him for the remainder of his life. In 1943 he was appointed to an

assistant professor Assistant professor is an academic rank just below the rank of an associate professor used in universities or colleges, mainly in the United States, Canada, Japan, and South Korea. Overview This position is generally taken after earning a doct ...

ship at

University of Vermont The University of Vermont and State Agricultural College, commonly referred to as the University of Vermont (UVM), is a Public university, public Land-grant university, land-grant research university in Burlington, Vermont, United States. Foun ...

. At National Research Council, by two years he worked with

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

and

Nelson Dunford Nelson James Dunford (December 12, 1906 – September 7, 1986) was an American mathematician, known for his work in functional analysis, namely vector measure, integration of vector valued functions, ergodic theory, and linear operators. The Dunf ...

. In 1946, he went to the

University of Kansas The University of Kansas (KU) is a public research university with its main campus in Lawrence, Kansas, United States. Two branch campuses are in the Kansas City metropolitan area on the Kansas side: the university's medical school and hospital ...

, first as

extraordinary professor Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

until 1952 and then as

ordinary professor Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

until 1961. He stayed at

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

in 1950 and 1952–1953, at

University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...

in 1960–1961, and at

State University of New York The State University of New York (SUNY ) is a system of Public education, public colleges and universities in the New York (state), State of New York. It is one of the List of largest universities and university networks by enrollment, larges ...

in 1961–1962. In 1962 he became professor at

Hunter College Hunter College is a public university in New York City, United States. It is one of the constituent colleges of the City University of New York and offers studies in more than one hundred undergraduate and postgraduate fields across five schools ...

, where he stayed until his death. Schatten widely studied

tensor product In mathematics, the tensor product V \otimes W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of ...

s of

Banach space In mathematics, more specifically in functional analysis, a Banach space (, ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and ...

s. In functional analysis, he is the namesake of the

Schatten norm In mathematics, specifically functional analysis, the Schatten norm (or Schatten–von-Neumann norm) arises as a generalization of ''p''-integrability similar to the trace class norm and the Hilbert–Schmidt norm. Definition Let H_1, H_2 be ...

and the Schatten class operators. His doctoral students included

Elliott Ward Cheney, Jr. Elliott Ward Cheney Jr. (June 28, 1929 – July 13, 2016) was an American mathematician and an emeritus professor at the University of Texas at Austin. Known to his friends and colleagues as Ward Cheney, he was one of the pioneers in the fields of ...

at University of Kansas, and Peter Falley and Charles Masiello at City University of New York. Schatten died in

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

in 1977.

References

External links

* {{DEFAULTSORT:Schatten, Robert Polish mathematicians 20th-century American mathematicians 1911 births 1977 deaths 20th-century Polish Jews University of Kansas faculty University of Southern California faculty State University of New York faculty Polish emigrants to the United States

Further reading

References

External links