Adriaan Cornelis "Aad" Zaanen (14 June 1913 in Rotterdam – 1 April 2003 in Wassenaar) was a Dutch mathematician working in analysis. He is known for his books on Riesz spaces (together with Wim Luxemburg).

Biography

Zaanen was born in Rotterdam, where he attended the Hogere Burgerschool. He graduated in 1930 with excellent marks, and started his studies in mathematics at

Leiden University Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...

. Having obtained his master's degree in 1935, he did research under the guidance of his

doctoral advisor A doctoral advisor (also dissertation director, dissertation advisor; or doctoral supervisor) is a member of a university faculty whose role is to guide graduate students who are candidates for a doctorate, helping them select coursework, as well ...

Johannes Droste, and was awarded a Ph.D. in 1938. His doctoral thesis dealt with the convergence of series of

eigenvalues In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...

s of the Sturm–Liouville type. The same year he was appointed a mathematics teacher at the Hogere Burgerschool in Rotterdam, a profession that he continued until 1947. In the next years and also in the period of the German occupation of the Netherlands, Zaanen continued to do mathematical research in his spare time. He studied Stefan Banach's ''Théorie des Opérations Linéaires'', the book that laid the foundations of functional analysis, and Marshall H. Stone's ''Linear Transformations in Hilbert Space''. During this period he wrote nine scientific papers on integral equations with symmetrisable kernels that were published in the Proceedings of the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...

in 1946-47. In parallel to his job as a secondary-school teacher, Zaanen was appointed in 1946 as a mathematics teacher for three hours per week at the

Technische Hogeschool Delft Delft University of Technology ( nl, Technische Universiteit Delft), also known as TU Delft, is the oldest and largest Dutch public technical university, located in Delft, Netherlands. As of 2022 it is ranked by QS World University Rankings among ...

, and as an unpaid ''privaatdocent'' at Leiden University where he taught a course on

Lebesgue integration In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis. The Lebesgue integral, named after French mathematician Henri Lebe ...

. In 1947 Zaanen accepted the position of Professor of Mathematics at the Technische Hogeschool Bandoeng. In 1950 he returned to the Netherlands where he was appointed Professor of Mathematics at the Technische Hogeschool Delft. In these years he continued his work on the book ''Linear Analysis'', which was published in 1953 and for years was a prominent work on functional analysis and the theory of integral equations. In 1956 Zaanen was appointed Professor of Mathematics at Leiden University. There he started a large research programme into the theory of Riesz spaces, together with his first doctoral student Wim Luxemburg, Professor of Mathematics at the California Institute of Technology. Most of their results were published in a series of papers in the Proceedings of the Royal Netherlands Academy of Arts and Sciences. Unusually for mathematics research in the Netherlands at the time, Zaanen pursued a long-term research programme involving a number of collaborators and doctoral students. Eight doctoral theses on various topics in the theory of Riesz spaces were produced in this school. Zaanen took retirement in 1982.

Publications

Zaanen published almost 70 papers in scientific journals and reviewed conference proceedings. He is however best known for four large books that each took a prominent place in scientific literature: * A.C. Zaanen, ''Linear Analysis'', North-Holland Publishing Company, Amsterdam and P. Noordhoff, Groningen (1953, 1957, 1960), 600 pages * Adriaan Cornelis Zaanen, ''Integration'', North-Holland Publishing Company, Amsterdam (1967) 604 pages. Revised and enlarged edition of ''An Introduction to the Theory of Integration'' (1958, 1961, 1965). * W.A.J. Luxemburg and A.C. Zaanen, ''Riesz Spaces Volume I'', North-Holland Publishing Company, Amsterdam London (1971), 514 pages * A.C. Zaanen, ''Riesz Spaces II'', North-Holland Publishing Company, Amsterdam New York Oxford (1983), 720 pages

Other functions and honours

Zaanen was elected a member of the

in 1960. He served as President of the Dutch Mathematical Society from 1970 until 1972. He was an editor of the Society's journal ''Nieuw Archief voor Wiskunde'' from 1953 until 1982. In 1988 he was appointed an honorary member of the Society. He served as a member of the ''Curatorium'' of the Mathematisch Centrum from 1965 until 1979. On his retirement in 1982 Zaanen was appointed Knight of the Order of the Netherlands Lion.

References

{{DEFAULTSORT:Zaanen, Adriaan Cornelis 1913 births 2003 deaths Dutch mathematicians Leiden University alumni Academic staff of the Delft University of Technology Academic staff of Leiden University Members of the Royal Netherlands Academy of Arts and Sciences Scientists from Rotterdam Knights of the Order of the Netherlands Lion Functional analysts