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ON STEFAN BANACH and SOME of HIS RESULTS 1 . Introduction Banach Journal of Mathematical Analysis I S Named After One of The

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ON STEFAN BANACH and SOME of HIS RESULTS 1 . Introduction Banach Journal of Mathematical Analysis I S Named After One of The ISSN sub h tt p : divided by hline to the power of Banach hline divided by B a n sub : slash 1 slash w from period m to 735 wn begin w hyphenf a l i 8787 g n ∗g open parenthesis a to the power of electronic sub t h hyphen a na ly s to the power of closing parenthesis i s periodISSN o ^ rgf toBanach the powerfn off r a c cf J n hr sub u l e Jf3em to thegf0.4 power pt g of gf periodB Math a o n uggg r n af periodh n subf r a c lf Analt t o f pperiod : subgf M n r 1 ua l e openf3emgf0.4 pt g gg^f a parenthesisc J f th hg to^f the. powerg f ofJ 2007g Math sub e mf ao t i to u the power r ofn closing a g parenthesis. f l commag Anal no cf a lo to the f powerg . off periodM g 1 sub1 f a g ( f t h g^f 2007 g^f ), g f e m a t i g no f c a l g^f . g 1 f A g , n ^f 1 g^f −− g f a g^f 1 g f l g^f 0 g f y g Banach ac J: Math : Anal : 1 (2007); no: 1 ;n1−−10 sis A comma n to the power of 1 subBa to n the powerhJ ofourn endash a l subof lM toa theth powere ma of ti 1 subca ly toA thea powerl y of 0 s i s s i s g f : f ISSN/ g 1ttp: f / g w ^f . m g f 735 f w w g − 8787 g ( f a g^f e l e c t r o n i c g^f ) g f t ON .. STEFAN .. BANACHh .. AND:=1 ..w SOME:m .. OF(electronic .. HIS) .. RESULTSis:org = 735ww−8787 a t h−a nalys h KRZYSZTOF− a na CIESIELSKI l y s tog thei power s of 1 . o rg g nendDedicatedf aON l i g n ∗g to Professor STEFAN Themistocles BANACH M period Rassias AND SOME OF HIS RESULTS Submitted by P period Enflo n centerlineAbstract periodfON ..nquad In theSTEFAN paper a shortnquad biographyBANACHKRZYSZTOFCIESIELSKI ofn Stefanquad BanachAND nquad comma1 SOME .. a fewnquad storiesOF nquad HIS nquad RESULTS g about Banach and the Scottish Caf acute-e and some results that nowadays are named n [ KRZYSZTOF CIESIELSKI ^Dedicatedf 1 g n ] to Professor Themistocles M . Rassias by Banach quoteright s surname are presentedSubmitted period by P . Enflo 1 period .. Introduction Abstract . In the paper a short biography of Stefan Banach , a few stories Banach Journal of Mathematical Analysis i s named after one of the most .... out hyphen n centerline f Dedicatedabout Banach to Professor and the Scottish Themistocles Cafe ´ and some M .results Rassias that nowadaysg are named standing mathematicians in the XXthby century Banach comma ' s surname Stefan Banach are presented period . .. Thus it is natural to .. recall .. in .. the .. first .. i ssue .. of the j ournal .. some .. information .. about .. Banach period .. A n centerline f Submitted by P . Enflo 1g . Introduction very shortBanach biography Journal comma of some Mathematical of his most eminent Analysis results i s named and some after stories one will of be the most out - presented in this article period n centerlinestandingf Abstract mathematicians . nquad In in the the paperXXth century a short , Stefan biography Banach of . Stefan Thus Banach it is natural , nquad a few stories g 2 periodto .. Banach recall and the in Scottish the .. Caf first e-acute i ssue of the j ournal some information Stefan Banach was born in the Polish city Krak acute-o w on 30 March comma .. 1 892 period .. Some n centerlineaboutf about Banach Banach . and A the very Scottish short biography Caf $ ,n someacute offe hisg $ most and eminent some results results and that nowadays are named g sources ..some give .. stories the .. date will .. be 20 presented .. March comma in this .. however article ... it .. was .. checked .. open parenthesis in particular comma .. in the n centerline fby Banach '2 s . surnameBanach are and presented the Scottish . g Caf e´ parish sourcesStefan by the Banach author .... was open born parenthesis in the open Polish square city bracket Krak 1 2o´ closingw on square 30 March bracket , closing 1 892 parenthesis . .... and by Roman Ka suppress-l u z-dotaccent a open parenthesis open square bracket 26 closing square bracket closing parenthesis closing n centerlineSomef1 . sourcesnquad Introduction give the dateg 20 March , however it was checked parenthesis ....( in that particular the date , in the 30 March is correct period nnoindentparishBanach sources Journal by the of author Mathematical ( [ 1 2 ] Analysis ) and by i Roman s named Ka after lu z_ a one ( [ 26 of ] the ) ) most that n h f i l l out − Banach quoterightthe date s parents were not married period .. It is not much known about his mother comma Katarzyna30 Banach March comma is correct after . whom he had a surname period .. It was j ust recently discovered nnoindentopen parenthesisstanding see open mathematicians square bracket 25 in closing the XXth square century bracket closing , Stefan parenthesis Banach that . shenquad was aThus maid itor servant is natural and to nquad r eBanach c a l l nquad ' s parentsin nquad werethe notn marriedquad f i . r s t Itnquad is noti much ssue knownnquad aboutof the his j mother ournal nquad some nquad information nquad about nquad Banach . nquad A Banach quoteright, s father comma Stefan Greczek comma who veryhline short biography , some of his most eminent results and some stories will be presentedKatarzyna in this Banach article , after . whom he had a surname . It was j ust recently discovered Date : Received( see [ 25: .. ] 1 ) 4 that June she 2007 was semicolon a maid Accepted or servant : 25 September and Banach 2007 ' period s father , Stefan Greczek , 2000 Mathematicswho Subject Classification period .. Primary 0 1 A 60 semicolon Secondary 46 hyphen 3 comma 46 B 25 period n centerlineKey words andf2 phrases. nquad periodBanach .. Banach and thecomma Scottish functionaln analysisquad Caf comma $ Scottishnacutef Cafeg acute-e$ g sub comma Lvov School of mathe hyphen Stefanmatics Banach comma Banach was born space in period the Polish city Krak $ nacutefog $ w on 30 March , nquad 1 892 . nquad Some s o1 u r c e s nquad g i v e nquad the nquad date nquad 20 nquad March , nquad however nquad i t nquad was nquad checked nquad ( in particular , nquad in the Date : Received : 1 4 June 2007 ; Accepted : 25 September 2007 . nnoindent parish sources by the author n h f i l l ( [ 1 2 ] ) n h f i l l and by Roman Ka n l u $ ndotfzg $ 2000 Mathematics Subject Classification . Primary 0 1 A 60 ; Secondary 46 - 3 , 46 B 25 . a ( [ 26 ] ) ) n h f i l l that the date Key words and phrases . Banach , functional analysis , Scottish Cafe ´; Lvov School of mathe - matics , Banach space . nnoindent 30 March is correct . 1 n hspace ∗fn f i l l gBanach ' s parents were not married . nquad It is not much known about his mother , nnoindent Katarzyna Banach , after whom he had a surname . nquad It was j ust recently discovered ( see [ 25 ] ) that she was a maid or servant and Banach ' s father , Stefan Greczek , who n begin f a l i g n ∗g n r u l e f3emgf0.4 pt g nendf a l i g n ∗g n centerline fDate : Received : nquad 1 4 June 2007 ; Accepted : 25 September 2007 . g n centerline f2000 Mathematics Subject Classification . nquad Primary 0 1 A 60 ; Secondary 46 − 3 , 46 B 25 . g Key words and phrases . nquad Banach , functional analysis , Scottish Caf $ nacutefeg f , g$ Lvov School of mathe − matics , Banach space . n centerline f1 g 2 .. K period CIESIELSKI nnoindentwas a soldier2 n openquad parenthesisK . CIESIELSKI probably assigned orderly to the officer under whom Katarzyna was a servant closing parenthesis .. could not .. marry Katarzyna because of some military rules period .. Banach nnoindent2was K .a CIESIELSKI soldier ( probably assigned orderly to the officer under whom Katarzyna was was grewwas up with a soldier the owner ( probably of the laundry assigned Franciszka orderly P suppress-lto the officer owa and under her niecewhom Maria Katarzyna period was Banach attended school in Krak o-acute w .. and took there final exams period .. He was .. in hyphen nnoindentaa servant servant ) could) nquad notcould marry not Katarzynanquad marry because Katarzyna of some military because rules of some. Banach military rules . nquad Banach t erestedwas in mathematics grew up with and he the was owner very good of the at laundryit period .. Franciszka However comma P lowa he thoughtand her that niece Maria . wasin this grew .. area up nothing with the .. much owner .. new of .. the can belaundry .. discovered Franciszka .. and .. he P ..n l decidedowa and to .. studyher niece .. at Maria . Banach attendedBanach attended school school in Krak in Krak $ nacuteo´ wfog and$ took w nquad thereand final took exams there . He final was exams in . nquad He was nquad in − the Technical- University at .. Lvov .. open parenthesis Politechnika Lwowska closing parenthesis period .. In those t imes both Krak o-acutet erested w and in Lvov mathematics were in the t and erritory he was governed very by good Austro at hyphen it . Hungary However period , he thought.. Therefore that nnoindentBanach movedt erested to Lvov period in mathematics .. His studies andthere he were was interrupted very good by the at First it World .
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