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, structure, space, models, and change. History On ...

. Robert Schatten was born to a Jewish family in

Lviv Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukrain ...

. His intellectual origins were at

Lwów School of Mathematics The Lwów school of mathematics ( pl, lwowska szkoła matematyczna) 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 ...

, 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 (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...

. His entire family was murdered during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

, he himself emigrated to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

. 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 (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

. 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 ...

, 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 academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors ...

ship, he joined the

United States army The United States Army (USA) is the land warfare, land military branch, service branch of the United States Armed Forces. It is one of the eight Uniformed services of the United States, U.S. uniformed services, and is designated as the Army o ...

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 and Canada. Overview This position is generally taken after earning a doctoral degree A docto ...

ship at

University of Vermont The University of Vermont (UVM), officially the University of Vermont and State Agricultural College, is a public land-grant research university in Burlington, Vermont. It was founded in 1791 and is among the oldest universities in the United ...

. At

National Research Council National Research Council may refer to: * National Research Council (Canada), sponsoring research and development * National Research Council (Italy), scientific and technological research, Rome * National Research Council (United States), part of ...

, by two years he worked with

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

and Nelson Dunford. 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, and several satellite campuses, research and educational centers, medical centers, and classes across the state of Kansas. T ...

, 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), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

in 1950 and 1952–1953, at

University of Southern California , mottoeng = "Let whoever earns the palm bear it" , religious_affiliation = Nonsectarian—historically Methodist , established = , accreditation = WSCUC , type = Private research university , academic_affiliations = , endowment = $8.1 ...

in 1960–1961, and at State University of New York in 1961–1962. In 1962 he became professor at Hunter College, where he stayed until his death. Schatten widely studied

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

s of Banach spaces. 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 H ...

and the Schatten class operators. His doctoral students included Elliott Ward Cheney, Jr. 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 or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

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

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