Alexandru Ghika (June 22, 1902 – April 11, 1964) was a

Romania Romania ( ; ro, România ) is a country located at the crossroads of Central Europe, Central, Eastern Europe, Eastern, and Southeast Europe, Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, S ...

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 ...

, founder of the Romanian school of

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 space#Definition, inner product, Norm (mathematics)#Defini ...

Life

He was born in

Bucharest Bucharest ( , ; ro, București ) is the capital and largest city of Romania, as well as its cultural, industrial, and financial centre. It is located in the southeast of the country, on the banks of the Dâmbovița River, less than north of ...

, into the

Ghica family The Ghica family ( ro, Ghica; sq, Gjika; el, Γκίκας, ''Gikas'') was a noble family active in Wallachia, Moldavia and in the Kingdom of Romania, between the 17th and 19th centuries. The Ghica family produced many voivodes of Wallachia and M ...

, the son of Ioan Ghika (1873–1949) and Elena Metaxa (1870–1951), and great-great-grandson of

Grigore IV Ghica Grigore IV Ghica or Grigore Dimitrie Ghica (June 30, 1755 – April 29, 1834) was Prince of Wallachia between 1822 and 1828. A member of the Ghica family, Grigore IV was the brother of Alexandru II Ghica and the uncle of Dora d'Istria. While many ...

Prince of Wallachia This is a list of rulers of Wallachia, from the first mention of a medieval polity situated between the Southern Carpathians and the Danube until the union with Moldavia in 1859, which led to the creation of Romania. Notes Dynastic rule is hard t ...

.Family tree
at ghika.org He started his secondary studies at the Gheorghe Lazăr High School in Bucharest. In 1917, he left with his family for

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

, completing his secondary studies at the

Lycée Louis-le-Grand The Lycée Louis-le-Grand (), also referred to simply as Louis-le-Grand or by its acronym LLG, is a public Lycée (French secondary school, also known as sixth form college) located on rue Saint-Jacques in central Paris. It was founded in the ...

in 1920. He then entered the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

(the Sorbonne) with a major in mathematics, graduating in 1922. In 1929, he obtained a

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

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 The University of Bucharest ( ro, Universitatea din București), commonly known after its abbreviation UB in Romania, is a public university founded in its current form on by a decree of Prince Alexandru Ioan Cuza to convert the former Princel ...

, working in the Function Theory section chaired by

Dimitrie Pompeiu Dimitrie D. Pompeiu (; – 8 October 1954) was a Romanian mathematician, professor at the University of Bucharest, titular member of the Romanian Academy, and President of the Chamber of Deputies. Biography He was born in 1873 in Broscăuți, ...

. 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 The Romanian Academy ( ro, Academia Română ) is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 active members who are elected for life. According to its byl ...

, and was promoted to full membership on March 20, 1963. In 1949, at the founding of the

Institute of Mathematics of the Romanian Academy The "Simion Stoilow" Institute of Mathematics of the Romanian Academy is a research institute in Bucharest, Romania. It is affiliated with the Romanian Academy, and it is named after Simion Stoilow, one of its founders. History On December 2 ...

, 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 A prime minister, premier or chief of cabinet is the head of the cabinet and the leader of the ministers in the executive branch of government, often in a parliamentary or semi-presidential system. Under those systems, a prime minister is not ...

Constantin Angelescu Constantin Angelescu (10 June 1869 – 14 September 1948) was a Romanian politician who served as ad interim/ acting Prime Minister of Romania for five days, between 30 December 1933 and 3 January 1934. He was: Doctor of Medicine in Paris, Pleni ...

) 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 Măgurele is a town situated in the southwestern part of Ilfov County, Muntenia, Romania. It has a population of 11,000 and hosts several research institutes. Research institutes The town hosts ''Măgurele Science Park'', the largest science par ...

. Alexandru Ghika died in Bucharest of

lung cancer Lung cancer, also known as lung carcinoma (since about 98–99% of all lung cancers are carcinomas), is a malignant lung tumor characterized by uncontrolled cell growth in tissue (biology), tissues of the lung. Lung carcinomas derive from tran ...

. He was buried at the Ghika-Tei

church Church may refer to: Religion * Church (building), a building for Christian religious activities * Church (congregation), a local congregation of a Christian denomination * Church service, a formalized period of Christian communal worship * Chris ...

, founded in 1833 by Prince

Grigore Alexandru Ghica Grigore Alexandru Ghica or Ghika (1803 or 1807 – 24 August 1857) was a Prince of Moldavia between 14 October 1849, and June 1853, and again between 30 October 1854, and 3 June 1856. His wife was Helena, a member of the Sturdza family and dau ...

. 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. Cabiria Andreian Cazacu, Romulus Cristescu, ''Alexandru Ghika (1902--1964)'', Gaz. Mat. Ser. A 70 (1965), 428--439. His research in functional analysis introduced new concepts, such as ''F''-

ordered ring In abstract algebra, an ordered ring is a (usually 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 ...

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 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 f ...

holds. He is also remembered for a

representation theorem In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure. Examples Algebra * Cayley's theorem states that every group i ...

for reflexive

Banach space In mathematics, more specifically in functional analysis, a Banach space (pronounced ) 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 vector ...

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.

References

External links

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Short biography
{{DEFAULTSORT:Ghika, Alexandru 20th-century Romanian mathematicians Mathematical analysts Titular members of the Romanian Academy Academic staff of the University of Bucharest University of Paris alumni Gheorghe Lazăr National College (Bucharest) alumni Alexandru Ghika Scientists from Bucharest 1902 births 1964 deaths Deaths from cancer in Romania Deaths from lung cancer Members of the Romanian Academy of Sciences Romanian expatriates in France