Robert Schatten
Encyclopedia
Robert Schatten was a Polish American
mathematician
.
Robert Schatten was born in Lwów. He received his magister
degree from Lwów University in 1933. After his emigration to the United States
he enrolled at Columbia University
and received his master's degree in 1939. He continued his research under the supervision of Francis J. Murray and received his doctorate degree in 1942. Shortly after being appointed to a junior professor
ship, he joined the army. During his army training he suffered a back injury which affected him for the remainder of his life.
In 1943 he was appointed to an assistant professorship at the University of Vermont
. He spent two years at the National Research Council
, where he worked together with John von Neumann
and Nelson Dunford
. In 1946, Schatten went to Kansas University, first as extraordinary professor until 1952, then as ordinary professor until 1961, with intermissions through stays at the Institute for Advanced Study
(1950 and 1952–1953). In 1960–1961 he spent a year at the University of Southern California
and in 1961–1962 he taught at the State University of New York
. In 1962 he became professor at Hunter College
, where he stayed until his death
Rober Schatten was Jewish; his entire family was murdered during World War II
.
Schatten's main field of mathematical studies was tensor products
of Banach spaces
. He is the namesake of the Schatten class operator
s.
Schatten died in New York City
in 1977.
Polish American
A Polish American , is a citizen of the United States of Polish descent. There are an estimated 10 million Polish Americans, representing about 3.2% of the population of the United States...
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....
.
Robert Schatten was born in Lwów. He received his magister
Magister (degree)
Magister is an academic degree used in various systems of higher education.-Argentina:...
degree from Lwów University in 1933. After his emigration to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
he enrolled at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
and received his master's degree in 1939. He continued his research under the supervision of Francis J. Murray and received his doctorate degree in 1942. Shortly after being appointed to a junior professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
ship, he joined the army. During his army training he suffered a back injury which affected him for the remainder of his life.
In 1943 he was appointed to an assistant professorship at the University of Vermont
University of Vermont
The University of Vermont comprises seven undergraduate schools, an honors college, a graduate college, and a college of medicine. The Honors College does not offer its own degrees; students in the Honors College concurrently enroll in one of the university's seven undergraduate colleges or...
. He spent two years at the National Research Council
United States National Research Council
The National Research Council of the USA is the working arm of the United States National Academies, carrying out most of the studies done in their names.The National Academies include:* National Academy of Sciences...
, where he worked together with John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
and Nelson Dunford
Nelson Dunford
Nelson Dunford was an American mathematician, known for his work in functional analysis, namely integration of vector valued functions, ergodic theory, and linear operators. The Dunford decomposition, Dunford–Pettis property, and Dunford-Schwartz theorem bear his name.He studied mathematics at the...
. In 1946, Schatten went to Kansas University, first as extraordinary professor until 1952, then as ordinary professor until 1961, with intermissions through stays at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
(1950 and 1952–1953). In 1960–1961 he spent a year at the University of Southern California
University of Southern California
The University of Southern California is a private, not-for-profit, nonsectarian, research university located in Los Angeles, California, United States. USC was founded in 1880, making it California's oldest private research university...
and in 1961–1962 he taught at the State University of New York
State University of New York
The State University of New York, abbreviated SUNY , is a system of public institutions of higher education in New York, United States. It is the largest comprehensive system of universities, colleges, and community colleges in the United States, with a total enrollment of 465,000 students, plus...
. In 1962 he became professor at Hunter College
Hunter College
Hunter College, established in 1870, is a public university and one of the constituent colleges of the City University of New York, located on Manhattan's Upper East Side. Hunter grants undergraduate, graduate, and post-graduate degrees in more than one hundred fields of study, and is recognized...
, where he stayed until his death
Rober Schatten was Jewish; his entire family was murdered during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
.
Schatten's main field of mathematical studies was tensor products
Tensor product
In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects. In each case the significance of the symbol is the same: the most general...
of Banach spaces
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...
. He is the namesake of the Schatten class operator
Schatten class operator
In mathematics, specifically functional analysis, a pth Schatten-class operator is a bounded linear operator on a Hilbert space with finite pth Schatten norm. The space of pth Schatten-class operators is a Banach space with respect to the Schatten norm.Via polar decomposition, one can prove that...
s.
Schatten died in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
in 1977.
Further reading
- A Theory of Cross-Spaces. Annals of Mathematics Studies, ISBN 0-691-08396-7
- Norm Ideals of Completely Continuous Operators. Ergebnisse der Mathematik und ihrer Grenzgebiete, 2. Folge, ISBN 3-540-04806-5