Alexandru Ghika
Encyclopedia
Alexandru Ghika was a Romania
n mathematician
, founder of the Romanian school of functional analysis
.
, into the Ghica family
, the son of Ioan Ghika (1873–1949) and Elena Metaxa (1870–1951), and great-great-grandson of Grigore IV Ghica
, Prince of Wallachia. He started his secondary studies at the Gheorghe Lazăr High School in Bucharest. In 1917, he left with his family for Paris
, completing his secondary studies at the Lycée Louis-le-Grand
in 1920. He then entered the University of Paris
(the Sorbonne) with a major in mathematics, graduating in 1922. In 1929, he obtained a Ph.D.
in mathematics from the Faculté des Sciences of the University of Paris.
After completing his doctorate, Ghika returned to Romania. In November 1932 he became Assistant Professor in the Mathematics Department of the University of Bucharest
, working in the Function Theory section chaired by Dimitrie Pompeiu
. On February 7, 1935, he was promoted to Associate Professor, and in 1945 he was named Full Professor and chair of the newly-founded Functional Analysis section.
In 1935, Ghika was elected corresponding member of the Romania Academy of Sciences, being promoted to full member in 1938. In 1955 he became corresponding member of the Romanian Academy
, and was promoted to full membership on March 20, 1963. In 1949, at the founding of the Institute of Mathematics of the Romanian Academy
, he became the chair of the Functional Analysis section of that Institute, a position he held till his death.
Ghika married Elisabeta Angelescu (daughter of one-time Prime Minister
Constantin Angelescu
) on June 7, 1934. They had a son, Grigore (born November 7, 1936), who became a researcher at the Institute of Atomic Physics in Măgurele
.
Alexandru Ghika died in Bucharest of lung cancer
. He was buried at the Ghika-Tei church
, founded in 1833 by Prince Grigore Alexandru Ghica
.
In March, 2007, the heirs of the Ghika and Angelescu families won back their rights to Hotel Lido, in Bucharest.
His research in functional analysis introduced new concepts, such as F-ordered ring
s (now known as Ghika rings), which have the property that in any module over a ring in this class, the analogue of the Hahn–Banach theorem
holds. He is also remembered for a representation theorem
for reflexive
Banach space
s, now known as the Ghika-James representation theorem.
Among his doctoral students were Silviu Teleman and Petru Mocanu.
Romania
Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...
n 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....
, founder of the Romanian school 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...
.
Life
He was born in BucharestBucharest
Bucharest is the capital municipality, cultural, industrial, and financial centre of Romania. It is the largest city in Romania, located in the southeast of the country, at , and lies on the banks of the Dâmbovița River....
, into the Ghica family
Ghica family
The Ghica family were a Romanian noble family, active in Wallachia, Moldavia and in the Kingdom of Romania. In the 18th century, several branches of the family went through a process of Hellenization...
, the son of Ioan Ghika (1873–1949) and Elena Metaxa (1870–1951), and great-great-grandson of Grigore IV Ghica
Grigore IV Ghica
Grigore IV Ghica or Grigore Dimitrie Ghica was Prince of Wallachia between 1822 and 1828. A member of the Ghica family, Grigore IV was the brother of Alexandru Ghica and the uncle of Dora d'Istria....
, Prince of Wallachia. He started his secondary studies at the Gheorghe Lazăr High School in Bucharest. In 1917, he left with his family for Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, completing his secondary studies at the Lycée Louis-le-Grand
Lycée Louis-le-Grand
The Lycée Louis-le-Grand is a public secondary school located in Paris, widely regarded as one of the most rigorous in France. Formerly known as the Collège de Clermont, it was named in king Louis XIV of France's honor after he visited the school and offered his patronage.It offers both a...
in 1920. He then entered the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
(the Sorbonne) with a major in mathematics, graduating in 1922. In 1929, he obtained a 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...
in mathematics from the Faculté des Sciences of the University of Paris.
After completing his doctorate, Ghika returned to Romania. In November 1932 he became Assistant Professor in the Mathematics Department of the University of Bucharest
University of Bucharest
The University of Bucharest , in Romania, is a university founded in 1864 by decree of Prince Alexander John Cuza to convert the former Saint Sava Academy into the current University of Bucharest.-Presentation:...
, working in the Function Theory section chaired by Dimitrie Pompeiu
Dimitrie Pompeiu
-Biography:After studying in Dorohoi and Bucharest, he went to France, where he studied mathematics at the University of Paris . He obtained a Ph.D. degree in mathematics in 1905 with a thesis, On the continuity of complex variable functions, written under the direction of Henri Poincaré...
. On February 7, 1935, he was promoted to Associate Professor, and in 1945 he was named Full Professor and chair of the newly-founded Functional Analysis section.
In 1935, Ghika was elected corresponding member of the Romania Academy of Sciences, being promoted to full member in 1938. In 1955 he became corresponding member of the Romanian Academy
Romanian Academy
The Romanian Academy is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 acting members who are elected for life....
, and was promoted to full membership on March 20, 1963. In 1949, at the founding of the Institute of Mathematics of the Romanian Academy
Institute of Mathematics of the Romanian Academy
The Institute of Mathematics "Simion Stoilow" of the Romanian Academy is a research institute in Bucharest, specialized in Mathematics. It was named after Simion Stoilow, who was its first Director, in 1949. In 1974 Nicolae Ceauşescu's daughter Zoia was permitted into the institute because of her...
, he became the chair of the Functional Analysis section of that Institute, a position he held till his death.
Ghika married Elisabeta Angelescu (daughter of one-time Prime Minister
Prime Minister of Romania
The Prime Minister of Romania is the head of the Government of Romania. Initially, the office was styled President of the Council of Ministers , when the term "Government" included more than the Cabinet, and the Cabinet was called The Council of Ministers...
Constantin Angelescu
Constantin Anghelescu
Constantin Angelescu was a Romanian politician who served as an interim Prime Minister of Romania for five days, between 30 December 1933 and 3 January 1934....
) on June 7, 1934. They had a son, Grigore (born November 7, 1936), who became a researcher at the Institute of Atomic Physics in Măgurele
Magurele
Măgurele is a town situated in the southwestern part of Ilfov County, Romania. Its population is 9,200. Four villages are administered by the town: Alunişu, Dumitrana, Pruni and Vârteju....
.
Alexandru Ghika died in Bucharest of lung cancer
Lung cancer
Lung cancer is a disease characterized by uncontrolled cell growth in tissues of the lung. If left untreated, this growth can spread beyond the lung in a process called metastasis into nearby tissue and, eventually, into other parts of the body. Most cancers that start in lung, known as primary...
. He was buried at the Ghika-Tei church
Romanian Orthodox Church
The Romanian Orthodox Church is an autocephalous Eastern Orthodox church. It is in full communion with other Eastern Orthodox churches, and is ranked seventh in order of precedence. The Primate of the church has the title of Patriarch...
, founded in 1833 by Prince Grigore Alexandru Ghica
Grigore Alexandru Ghica
Grigore Alexandru Ghica or Ghika was a Prince of Moldavia between October 14, 1849 and June 1853, and again between October 30, 1854 and June 3, 1856...
.
In March, 2007, the heirs of the Ghika and Angelescu families won back their rights to Hotel Lido, in Bucharest.
Legacy
Ghika introduced the study of functional analysis in Romania at a time when it was still a new field of mathematics. As a professor at the University of Bucharest, he was an important promoter of the Bourbaki rigorous approach to mathematics. His collected works number 103 published articles and books, 10 manuscripts, and 25 didactic works.His research in functional analysis introduced new concepts, such as F-ordered ring
Ordered ring
In abstract algebra, an ordered ring is a commutative ring R with a total order ≤ such that for all a, b, and c in R:* if a ≤ b then a + c ≤ b + c.* if 0 ≤ a and 0 ≤ b then 0 ≤ ab....
s (now known as Ghika rings), which have the property that in any module over a ring in this class, the analogue of the Hahn–Banach theorem
Hahn–Banach theorem
In mathematics, the Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear functionals defined on a subspace of some vector space to the whole space, and it also shows that there are "enough" continuous linear functionals defined on every normed...
holds. He is also remembered for a representation theorem
Representation theorem
In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to a concrete structure.For example,*in algebra,...
for reflexive
Reflexive space
In functional analysis, a Banach space is called reflexive if it coincides with the dual of its dual space in the topological and algebraic senses. Reflexive Banach spaces are often characterized by their geometric properties.- Normed spaces :Suppose X is a normed vector space over R or C...
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...
s, now known as the Ghika-James representation theorem.
Among his doctoral students were Silviu Teleman and Petru Mocanu.
Works
- Sur les fonctions de carré sommable le long des contours de leur domaines d’holomorphisme et leur applications aux équations différentielles linéaires d’ordre infini, Ph.D. thesis, Faculté des Sciences de Paris, 1929.
- On reflexive Banach spaces, Acad. Repub. Pop. Române. Bul. Şti. A. 1 (1949), 639—644.
- The extension of general linear functionals in semi-normed modules, Acad. Repub. Pop. Române Bul. Şti. Ser. Mat. Fiz. Chim. 2 (1950), 399—405.
- Analizǎ funcţionalǎ (Functional analysis), Editura Academiei Republicii Socialiste România, Bucharest, 1967.
- Opera matematicǎ (Mathematical works), Editura Academiei Republicii Socialiste România, Bucharest, 1968.