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.https://mathgenealogy.org/id.php?id=8598 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 
Sõsg ning b sẽn gʋlsã " tõe n yɩɩ sõma tɩ karen-bi-kãensã wʋsg pa tõe n wʋm ye". Sõng-y tɩ y maneg-a n kɩt tɩ ned sẽn pa bãng-a wã wʋm a võore, la y pa yiisd bãngr-goamã ye. (yʋʋmd 2025) (Learn how and when to remove this message)

 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