Alexandra Bellow

**Alexandra Bellow** (née **Bagdasar**; sen da booni **Ionescu Tulcea**; August 30, 1935 – May 2, 2025) A ra yaa Romã-Amerik neda sẽn yaa matematɛk soab sẽn maan a sẽn tõe n maan bũmb nins sẽn yaa a sẽn tõe tɩ yɩ a sẽn tõe t'a bãng a sẽn tõe to-to wã.

## Biography

A Bellow rogame Bucharest, Romayn soolmẽ wã, yʋʋmd 1935 t'a yʋʋr boond t'a Alexandra Bagdasar. A roagdbã fãa ra yaa logtoɛɛmbã. A ma, a Florica Bagdasar (a sẽn dog a Ciumetti) ra yaa kom-pugl tɩɩm karen-saamb. A ba wã, a Dumitru Bagdasar, ra yaa neurokirɛɛg. A paama a M.S. wã matematikkã pʋgẽ Bucharest karẽn-biis roogẽ yʋʋmd 1957, a sẽn yã la a kẽ kãadem ne a sɩdã, matematikkã Cassius Ionescu-Tulcea. A kẽnga ne a sɩdã Etazĩni yʋʋmd 1957 wã, la a paama a PhD wã Yale Yuniovɛrsẽ yʋʋmd 1959 wã, a Shizuo Kakutani sẽn wilg-a t'a na n maan a tʋʋm-no-kãnga. A sẽn paam a diplôme wã poore, a tʋma wa yel-bũndã karen-biis a Yale yʋʋmd 1959 n tãag yʋʋmd 1961 wã, la a yaa karen-bi-bi-pugl sẽn sõng Pennsylvania Yunivɛrzitetã yʋʋmd 1962 n tãag afe 1964 wã. Yʋʋmd 1964 n tãag 1967, a yɩɩ karẽn-soab Illinois karẽn-biis roogẽ. Yʋʋmd 1967 wã, a kẽnga Northwestern University n lebg matematikk karen-saamb. A zĩnda Northwestern wã hal n tãag a sẽn yi a yõor yaoogẽ yʋʋmd 1996, t'a lebg karen-saamb sẽn yaa karen-bi-poak.

A sẽn kẽ kãadem ne a Cassius Ionescu-Tulcea (1956-1969), yẽ ne a sɩdã gʋlsa tʋʋm wʋsg la vaeesg sebr sẽn gomd tõog wɛɛngẽ.

A Alexandra sɩdã a yiib-n-soabã yaa gʋlsd a Saul Bellow, sẽn paam a Nobel kũunã yʋʋmd 1976 wã pʋgẽ, b kãadmã wakate (1975-1985). A Alexandra yaa a Bellow sẽn gʋlsã pʋgẽ. A sẽn gʋls a Nowɛllã pʋgẽ, a sẽn boond t'a "To Jerusalem and Back" (1976), la a Nowɛl ning a sẽn boond tɩ "The Dean's December" (1982), a sẽn gʋls yʋʋm wʋsg b kãadmã kaoob poore, a Ravelstein (2000) pʋgẽ, a yɩɩ nowɛll sẽn yaa satirik n yɩɩd rẽ. Yʋʋmd 1990 wã yʋʋm kob-gĩndẽ wã, a Alexandra paama sũ-noog wʋsgo, a sẽn kẽ kãadem ne matematɛk soab a Alberto P. Calderón yʋʋmd 1989 wã yĩnga.

A Bellow kiime Chicago, Illinois yʋʋmd 2025 soabã, kiuug rasem 2 yʋʋm 89.

## Mathematiki tʋʋmd

### Lifting theory
A sẽn sɩng tʋʋm kẽer pʋgẽ, a ra tara bũmb wʋsg n tõe n wa maane, la a ra tara a sẽn na n tall-b n zẽk-b to-to wã. A John von Neumann la a Dorothy Maharam sẽn sɩng n maand tʋʋm-kãsemse, a Ionescu Tulceas tʋʋm n kõ-a a meng yʋʋm 1960 la 1970 wã pʋgẽ, n kõ-b sor n na n wilg tɩ bũmb nins sẽn maand ne a sẽn tõe n yɩ to-to wã yaa a sẽn na n maan to-to. B sẽn gʋls b Result monograph wã yʋʋmd 1969 wã lebga kɩbay sẽn yaa sõma zĩ-kãnga.

B sẽn dɩk n zẽk n kõ stochasticã sẽn maandã, Ionescu Tulceas wã paama "dɩtg sẽn tõe n welg" bũmb ning sẽn maandã. Woto kõta kaset sẽn yaa tao-tao ne Joseph Leo Doob sẽn yeel tɩ bũmb ning sẽn tõe n toeem tɩ b welg-a wã pa be (a sẽn tõe n maan woto wã me yaa "dɩta" sẽn tõe n kɩt tɩ b welg tɩ b welg bũmb ningã). Sẽn paase, ned sã n dɩkd a sẽn tõe n dɩk n zẽk a sẽn tõe ne "kẽeng" n makd bũmb ning sẽn tar yõod wʋsg Banach space zĩiga pʋgẽ, a paamdda a sẽn tõe t'a makd bũmb wʋsg n paase; rẽ kõta a Phillips sẽn yet tɩ yaa tõ-kãseng a yembr n wilgd t'a sẽn tõe n makd a sẽn maand to-to wã yaa sõma (a leb n yaa "kẽng" n tõe n paam n makd-a to-to).

D yetame tɩ tʋʋm sẽn tõe n makd a ye sẽn yaa H wã pidsda "bɩg-bɩɩg" ning b sẽn boond tɩ "bɩɩg-bʋʋg" wã, sã n yaa tɩ tʋʋm a yiib sẽn yaa toor sẽn be H pʋgẽ wã kẽeda taab sẽn yaa toor-toorã sʋka. D sã n dat n bãng tɩ d tõe n maana bũmb sẽn yaa sõma, d segd n bao n bãngame tɩ d tõeeme n maan bũmb sẽn yaa sõama. "Tõnd sẽn tõe n tall n tall n zẽk n zẽkd bũmbã" wã wilgda bũmb ning sẽn kɩt tɩ tʋʋm nins sẽn be zẽedã zĩigẽ wã maand sõma n yɩɩd woto. Bɩ d kõ H wã yɩ tʋʋm sẽn tõe n mak ne bũmb nins sẽn pʋgdã: (I) H yaa kompaakt (b sẽn get b sẽn tõe n maan to-to n bãng b sẽn tõe tɩ b sõsd to-to wã) (II) H yaa sẽn yaa kongr (convex); (III) H pidsda "b sẽn tõe n welg to-to" wã. Rẽ n so tɩ H yaa metr. A Ionescu Tulceas sẽn wilg tɩ b sẽn dɩkd b sẽk n dɩkd b mens n kẽng n kẽng n tɩ kẽng n kẽng tẽngẽ wã, b sẽn lebg n dɩkd a soab n dɩkd n kẽng n dɩkd sor n kẽng n kẽnd n kẽng n getẽ wã, pa mak-y ye.

### Martingales
Yʋʋmd 1960 wã sɩngrẽ, a ra tʋmd ne a C. Ionescu Tulcea n maand Martingales sẽn dɩkd b yõodo. La ne yam a yembre, tʋʋm-kãngã kɩtame tɩ b sɩng n zãmsda Martingales sẽn tar vektɛɛr yõodã, n wilg tɩ b sẽn maan bũmb ning fãa wã yaa tɩ b "tõnd" sẽn get Martingalesã sẽn get bũmb nins sẽn be Banach pʋgẽ wã, tɩ b get-a wa Radon-Nikodym sẽn yaa bũmb ning n kɩt tɩ b bãngd bũmb ning sẽn be a pʋgẽ wã. A Bellow yaool n paasame tɩ b bãng tɩ b ra tara "tõnd sẽn yaa toor-toore", (a Banach sẽn yaa zĩigã pʋgẽ, tõnd sẽn ya toor-toorã yaa Martingales, quasi-Martingales la b tara bãag sẽn yaa kãseng n paasd b sẽn tõe n tall n tall n paame, wala makre, b sẽn yãkd b toor-toora wã), la masã yaa sak sẽn tar yõod wʋsg probabillã wɛɛngẽ.

### Ergodic theory
Yʋʋmd 1960 wã, a Donald Samuel Ornstein maana lebgr sẽn pa be a Lebesgue space wã pʋgẽ, sẽn pa kõt -finite invariant sẽn yaa Lebesgue sẽn yaa to-to wã wɛɛngẽ, n welg zu-loees sẽn kaoosd a Ergodic teori wã pʋgẽ. Yʋʋm a wãn poore, a Rafael V. Chacón kõo mak-sõng sẽn wilgd tɩ ned kam fãa sẽn get a Zeova yell n pa tõe n maan bũmb ning a sẽn datã. A tʋʋmdã kɩtdame tɩ bõn-kãens fãa lebg taaba. A wilgame tɩ b sẽn tũnugd ne Baire sullã manesem n wilg tɩ b sẽn da get tɩ b yaa toor-toorã n pa tar rogem-n-tɩrgã makrã, a Ornstein n deng n yã, la a Chacón n yaool n yã wã yaa sɩd-sɩd la b sẽn da yã wã.

Yʋʋmd 1980 wã sɩngrẽ, a Bellow sɩngame n yiis seb-kãensã sẽn kɩt tɩ b vʋʋg Ergodik raabã sẽn gomd limit teoremã la pointwise wã yellã. Woto paama b sẽn na n maan ne a sẽn na n dɩk a sẽn tõe n maan bũmb ninsã la a sẽn na yɩl n bãng a sẽn tõe t'a maan bũmb ninsã, la a sẽn tõe ne a sẽn tõe fãa wã. A sẽn wa n gom "Tõog ning b sẽn getã" yellã, a sẽn wa n sõs ne a karen-bi-poakã yʋʋmd 1981 wã, a ra gomda bũmb a yiib yelle. A ra gomda bũmb ning sẽn yaa "tõog ning sẽn getã", la bũmb a taab sẽn getã yelle. La yʋʋm wʋsg poore, a Jean Bourgain reega yell kãngã, sẽn yaa "kwadr" wã wɛɛngẽ, la "prɛmsã" wɛɛngẽ (Máté Wierdl n wilg tɩ b pa tõe n maan bũmb ning ye; la a pa reega rẽ ye). A Bourgain paama a Fields medal yʋʋmd 1994 wã, a sẽn maan tʋʋmd a woto wã yĩnga.

Yaa a Ulrich Krengel n deng n kõ yʋʋmd 1971 wã, a sẽn maan n paasd a sẽn tar sõor sẽn yaa sõma wã siglgã sẽn tar pãng n paas tɩ b tõe n bãng tɩ b pa tõe n maan bũmb nins sẽn yaa sõma n kɩt tɩ b lebg n lebg n lebg toɛy-toɛyã ye. "Bõn-wẽng" woto sẽn be dũniyã gill zugã pa yɩk-m-la ne rabeem ye. A Bellow wilgame tɩ sõrb sõor sẽn yaa sõma fãa yaa "vɩɩm sõor sẽn pa sõma" pʋgẽ. Woto yĩnga, "vẽng-vẽng" sẽn yaa "vẽnge" yaa mak-sõngo. Rẽ poore, a tõog n wilg tɩ b sẽn get bũmb ning sẽn yaa ergodik teoremã wɛɛngẽ wã, sõor sẽn yaa sõma tõe n yɩɩ "tõnd fãa" pʋgẽ, la "tõnda fãa" pʋgẽ. Rẽ sɩd ling-a lame, la a leokame sok-kãngã a Roger Jones sẽn sokã.

D sã n dat n bãng tɩ b yaa neb sẽn tar pãng n maand bũmbu, d tõe n bãnga b sẽn maand to-to wã võore. Woto wilgda yɛlã sẽn yaa to-to wã, zĩig fãa, b sẽn pa tõe n maan bũmb n zemsd taab to-to. A gʋlsa a sɛbã pʋsẽ. "Tõnd sẽn tar pãng n tõe n paam bũmb ninsã" tara yõod wʋsg vaeesg kãngã wɛɛngẽ. A Bellow ne a tʋmd-n-taas maana vaeesg sẽn yaa sõma la sẽn yaa sõma n wilg tɩ b tara noy toor-toor la makr wʋsg sẽn wilgd tɩ b tara pãng n tar b mensã. A sẽn da tʋmd ne a Krengel wã, a tõog n leok a Eberhard Hopf sẽn da tagsd bũmb ningã tɩ pa sõma. Rẽ poore, a Bellow ne a Krengel sẽn tʋmd ne a Calderón wã tõog n wilg tɩ sɩd yaa a Hopf rãmb n tar "tõnd sẽn tar pãng n tar pãng" wã.

Sã n yaa ne b sẽn zãmsd b sẽn maand b toorẽ wã, b sã n dɩkd b sẽn maand to-to wã wakat fãa, wala makre, b sãn yaa sõma n wa n wa n pa tarẽ wã, pa kɩtd tɩ b wa n wa ne taab ye. Woto wilgdame tɩ b tõe n maan yel-wẽn-kãsemse, b sã n wa tũnug ne Ergodik teoremã sẽn na yɩl n zãms bũmb nins sẽn be yĩng pʋgẽ wã. Rẽ tõe n nafame tɩ bãngdb la bãngdb bãngd b sẽn maan bũmb ninsã. Sẽn na yɩl n bãng sẽn yaa to-to wã, d tõe n bãnga bũmb nins sẽn be b sẽn maand to-to wakatẽ wã. Woto bee bloogã sẽn tar a to wã zug n paas.

Bãngdb wʋsg (a sẽn tar a Bourgain me) tʋma ne Zu-soabã sẽn da wa n sokd-a sogs-kãensã zugu, la b leok-b-la b sogsg kãens b sɛbã pʋgẽ.

## Kuun-ramb a sen paam lekolle puga

* yʋʋmd 1977–80 sulli, Visiting Committee, Harvard University Mathematics Department
* yʋʋmd 1980 Fairchild Distinguished Scholar Award, California Institute of Technology, Winter Term
* yʋʋmd 1987 Humboldt Prize, Alexander von Humboldt Foundation, Bonn, Germany
* yʋʋmd 1991 Emmy Noether Lecture, San Francisco
* yʋʋmd 1997 International Conference in Honor of Alexandra Bellow, on the occasion of her retirement, held at Northwestern University, October 23–26, 1997. A Proceedings of this Conference appeared as a special issue of the Illinois Journal of Mathematics, Fall 1999, Vol. 43, No. 3.
* yʋʋmd  2017 class of Fellows of the American Mathematical Society "for contributions to analysis, particularly ergodic theory and measure theory, and for exposition".

## A editoral tʋʋmd sẽn yaa sõma

* 1974–77 Editor, Transactions of the American Mathematical Society
* 1980–82 Associate Editor, Annals of Probability
* 1979– Associate Editor, Advances in Mathematics

## Ges-y me

* Saul Bellow 

= Sebtiise =